{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0001","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"187c2aa29cf606c36ebeb04aa183236fd57fbb44c864a26c85af29773a8b7a7c","family_id":"qf-density14-angle-split-candidate","seed":202610141001,"semantic_template":"qf-density14-angle-split-candidate/[\"0\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=0, candidate first=0. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 0)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 0)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0002","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd03d5edbf40e8884d2697503043e8080f3a8c0eed621744fb4df74453dab719","family_id":"qf-density14-angle-split-candidate","seed":202610141002,"semantic_template":"qf-density14-angle-split-candidate/[\"45\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=45. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 45)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 45)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0003","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0df48bf74bfccd4cb0eeaeb531fda1a880b9388088024a93798478009bfaea44","family_id":"qf-density14-angle-split-candidate","seed":202610141003,"semantic_template":"qf-density14-angle-split-candidate/[\"150\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=180, candidate first=30. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 150)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 150)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0004","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0b32b2f14951458048e4831f54340911f091c1988eea2d24d638acf0d06b14e","family_id":"qf-density14-angle-split-candidate","seed":202610141004,"semantic_template":"qf-density14-angle-split-candidate/[\"91\",false]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=-1. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(No, 91)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (No, 91)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0005","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7fc630c2e18fd628edc49028b79f5b41ccdb81cc126806644f215abb32fe55cd","family_id":"qf-density14-angle-split-candidate","seed":202610141005,"semantic_template":"qf-density14-angle-split-candidate/[\"-10\",false]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=100. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(No, -10)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (No, -10)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0006","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53247b0b2df69344d7616af5927f1e6d3670b31684290b17cea3569346bf663a","family_id":"qf-density14-angle-split-candidate","seed":202610141006,"semantic_template":"qf-density14-angle-split-candidate/[\"6\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=84. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 6)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 6)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0007","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82e7cec9866c46de8b4c5ac5a1b682dd7980c40216987dc9743180cea108080a","family_id":"qf-density14-angle-split-candidate","seed":202610141007,"semantic_template":"qf-density14-angle-split-candidate/[\"7\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=83. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 7)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 7)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0008","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64b771e96bc4f2cd7adb280cdc77942216847824cee7135e5cc78c5b5b60516f","family_id":"qf-density14-angle-split-candidate","seed":202610141008,"semantic_template":"qf-density14-angle-split-candidate/[\"8\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=82. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 8)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 8)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0009","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e6751ca71c1eec2f4518c73b25968043cffb872ba6b91702285fe5d4309b685","family_id":"qf-density14-angle-split-candidate","seed":202610141009,"semantic_template":"qf-density14-angle-split-candidate/[\"9\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=81. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 9)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 9)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0010","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"499dd04ce0b820f2b9c7bf4826661e15a213ff34bd98bd30dc44d5a7da9963d0","family_id":"qf-density14-angle-split-candidate","seed":202610141010,"semantic_template":"qf-density14-angle-split-candidate/[\"10\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=80. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 10)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 10)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0011","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"58fe0c57ea7f33a7c24da6231dc41708d5e950a8d97117487e611ce0a566acfd","family_id":"qf-density14-angle-split-candidate","seed":202610141011,"semantic_template":"qf-density14-angle-split-candidate/[\"11\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=79. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 11)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 11)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0012","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67228f2148b028f98c9ea279ff9ec9c15a0342a92aa19b7cdc9a9f60e482c11a","family_id":"qf-density14-angle-split-candidate","seed":202610141012,"semantic_template":"qf-density14-angle-split-candidate/[\"12\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=78. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 12)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 12)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0013","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"959503ef423fb840ef755e8d1204bf32f0e01c88088c1dc706f9b197c5fa5b49","family_id":"qf-density14-angle-split-candidate","seed":202610141013,"semantic_template":"qf-density14-angle-split-candidate/[\"13\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=77. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 13)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 13)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0014","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bda11e4110f2f141d2385118a45d5020a33b590605fe98c533a56bed64b9400e","family_id":"qf-density14-angle-split-candidate","seed":202610141014,"semantic_template":"qf-density14-angle-split-candidate/[\"14\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=76. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 14)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 14)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0015","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9915bf01e2d63136be9b8f7ecb1c40d032a11ee7fc947ff018bc6dd5487d7e02","family_id":"qf-density14-angle-split-candidate","seed":202610141015,"semantic_template":"qf-density14-angle-split-candidate/[\"15\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=75. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 15)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 15)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0016","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"daf4dcc2a0819998eb9ab8f36ed64561caa173e6c9f73a780683fb496eed6f65","family_id":"qf-density14-angle-split-candidate","seed":202610141016,"semantic_template":"qf-density14-angle-split-candidate/[\"16\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=74. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 16)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 16)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0017","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6c814e0455666084157c0d305d28479e0e2e9f37da29d0a66c187a386a31d7c","family_id":"qf-density14-angle-split-candidate","seed":202610141017,"semantic_template":"qf-density14-angle-split-candidate/[\"17\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=73. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 17)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 17)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0018","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8baa29fed95a5cb39e44eaf5cc370ca53ca3393480eba6cfa629bcb15929b60","family_id":"qf-density14-angle-split-candidate","seed":202610141018,"semantic_template":"qf-density14-angle-split-candidate/[\"18\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=72. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 18)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 18)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0019","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6b4b218baba438246c8229dd56875a4670bb72c72ddd8a67e74fc9046b7e321","family_id":"qf-density14-angle-split-candidate","seed":202610141019,"semantic_template":"qf-density14-angle-split-candidate/[\"19\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=71. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 19)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 19)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0020","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a6af2785d40c0439f8b2271ffc35003ed34725d608b195111513460b5c16e2c","family_id":"qf-density14-angle-split-candidate","seed":202610141020,"semantic_template":"qf-density14-angle-split-candidate/[\"20\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=70. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 20)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 20)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0021","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4555964f0ffb2d4aca0d1422e86e8dbca9d39eec2cea3d9037ac2831c0d25f1","family_id":"qf-density14-angle-split-candidate","seed":202610141021,"semantic_template":"qf-density14-angle-split-candidate/[\"21\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=69. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 21)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 21)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0022","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dbda03448f3148024ff7b16da4f7a34dc2f258e77c647112602cf8dbba01e308","family_id":"qf-density14-angle-split-candidate","seed":202610141022,"semantic_template":"qf-density14-angle-split-candidate/[\"22\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=68. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 22)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 22)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0023","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a120204a4d1c169077e639be1ad8284b228929af7fbbb8ff269e62eac034e36d","family_id":"qf-density14-angle-split-candidate","seed":202610141023,"semantic_template":"qf-density14-angle-split-candidate/[\"23\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=67. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 23)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 23)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0024","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ea1952bf0f8230dba2d57035e36f57e57ee456a498bf98fd576c606dcdbfdd71","family_id":"qf-density14-angle-split-candidate","seed":202610141024,"semantic_template":"qf-density14-angle-split-candidate/[\"24\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=66. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 24)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 24)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0025","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a864989ac3304338c7d2cf427a420e7e561a5ea930dc00d4012bb6c0e6a50ffc","family_id":"qf-density14-angle-split-candidate","seed":202610141025,"semantic_template":"qf-density14-angle-split-candidate/[\"25\",true]"},"fields":{"title":"Angle-Split Eligibility and Signed Remainder","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=65. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.","answer":{"kind":"expression","value":"(Yes, 25)","explanation":"Check the candidate range before exact subtraction; finite arithmetic is not a ray-measure proof. The exact result, retaining the requested order, is (Yes, 25)."},"skills":["Angle-Split Eligibility and Signed Remainder"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0026","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"118edee903dff201a72599e9c881e3726c7e9c7e25d370730146013f960f5762","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141026,"semantic_template":"qf-density14-angle-complement-supplement-pair/0"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=0. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 90, 180)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 90, 180)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0027","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40863f0e2c8f90b666ce7db9a0ee268fb1a9b1c6cfb82b16df0e4da264b20adc","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141027,"semantic_template":"qf-density14-angle-complement-supplement-pair/90"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=90. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 0, 90)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 0, 90)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0028","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e0f22a62a36902061e33bad03adeebda9b79e8e5754af6e950a92240f12a56d","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141028,"semantic_template":"qf-density14-angle-complement-supplement-pair/180"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=180. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(No, none, 0)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (No, none, 0)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0029","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b34fda2112c6233af4992707971d4cc49636e1401ce8689cfbc845c469a059d","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141029,"semantic_template":"qf-density14-angle-complement-supplement-pair/4"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=4. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 86, 176)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 86, 176)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0030","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf57475f44a6af4dedb973e8cc60d72addc55a794683ec795c18fe4cdba39826","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141030,"semantic_template":"qf-density14-angle-complement-supplement-pair/5"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=5. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 85, 175)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 85, 175)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0031","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"960ec8340fcc173d81e4b2f5516b618039e7e488680c1fac06dd5daf3873217c","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141031,"semantic_template":"qf-density14-angle-complement-supplement-pair/6"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=6. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 84, 174)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 84, 174)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0032","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d842e1b4ce15397f98081860d966230eba37bd9175e3c5269ea4d5042b8334b","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141032,"semantic_template":"qf-density14-angle-complement-supplement-pair/7"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=7. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 83, 173)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 83, 173)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0033","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf66d9934420de49b3936b740a0e986b6ccb60c066bca871bbbf2ee8a9510364","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141033,"semantic_template":"qf-density14-angle-complement-supplement-pair/8"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=8. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 82, 172)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 82, 172)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0034","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1c072326998c5f9befcad2a0c73117e4b5c24f01fc5f24533b79f3708733dcd","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141034,"semantic_template":"qf-density14-angle-complement-supplement-pair/9"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=9. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 81, 171)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 81, 171)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0035","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68958d8bb65c4201733647ff1b6003b5ba44ca53e174634d2693a6fee790fdd7","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141035,"semantic_template":"qf-density14-angle-complement-supplement-pair/10"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=10. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 80, 170)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 80, 170)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0036","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8e70c01fe6fe67ae62c67c7fd0cb0eaea4b89cc5691f46be40aef945fca3fc1","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141036,"semantic_template":"qf-density14-angle-complement-supplement-pair/11"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=11. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 79, 169)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 79, 169)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0037","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b817bcd18a4fcf8ed619e3e6d855907afbaeb090f646355533ad0e414e6f349","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141037,"semantic_template":"qf-density14-angle-complement-supplement-pair/12"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=12. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 78, 168)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 78, 168)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0038","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bd5de53070e6dd5b9c9acaf675f3f7e2f77614aecd112459b39732974386e62","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141038,"semantic_template":"qf-density14-angle-complement-supplement-pair/13"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=13. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 77, 167)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 77, 167)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0039","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc7fc8d394d605e2bbfc397d7fa6d6d89b7874d8af6f668390cece0b10990fa5","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141039,"semantic_template":"qf-density14-angle-complement-supplement-pair/14"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=14. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 76, 166)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 76, 166)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0040","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fbb6134cc25c909514214ca5603260c251b481909d99ce15a147053e5be3ec5","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141040,"semantic_template":"qf-density14-angle-complement-supplement-pair/15"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=15. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 75, 165)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 75, 165)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0041","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2496cf682c1d6e82ef8437cc1f5409a02fe1689736f1420012d13de10ca50dff","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141041,"semantic_template":"qf-density14-angle-complement-supplement-pair/16"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=16. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 74, 164)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 74, 164)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0042","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4d1d97aa5c3629dd22b65eee95cfd64d3f117480eaa75c0046fd63235a78be1","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141042,"semantic_template":"qf-density14-angle-complement-supplement-pair/17"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=17. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 73, 163)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 73, 163)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0043","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d2f0111fc6ae3813c6c0e7f4cdf63fc92611f9284fb8c107f9e2ee47b2da6ff7","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141043,"semantic_template":"qf-density14-angle-complement-supplement-pair/18"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=18. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 72, 162)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 72, 162)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0044","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01690a561568a4a4d455f74ac0f3fe7eab4d9558868675787370d1d040564108","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141044,"semantic_template":"qf-density14-angle-complement-supplement-pair/19"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=19. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 71, 161)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 71, 161)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0045","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"283ffaf6dd3179efd86fe3831206f9641fe1d5ba12e149e1354bd2c50754f0e1","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141045,"semantic_template":"qf-density14-angle-complement-supplement-pair/20"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=20. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 70, 160)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 70, 160)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0046","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96baa4750017948ae8f21a0e5e2f1bf67403084aeca10f83a5b046fee92a40a6","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141046,"semantic_template":"qf-density14-angle-complement-supplement-pair/21"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=21. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 69, 159)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 69, 159)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0047","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a2655d0f23ea16405e4d846a214845a999baede18a2243e26964fec13dbba58a","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141047,"semantic_template":"qf-density14-angle-complement-supplement-pair/22"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=22. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 68, 158)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 68, 158)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0048","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5af1b5c1a752b5f3c22ae598d7f5e8426e170cd00da00190210834886158c7c1","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141048,"semantic_template":"qf-density14-angle-complement-supplement-pair/23"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=23. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 67, 157)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 67, 157)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0049","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12953ab45b71911c3b12f46ed1965c660f796cea33ef5011baa3279b33ac71ca","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141049,"semantic_template":"qf-density14-angle-complement-supplement-pair/24"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=24. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 66, 156)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 66, 156)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0050","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"caf1d315689ff5a6b7ef66d2bbada20f9a997a41998b61d9784146a30c52a6ca","family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141050,"semantic_template":"qf-density14-angle-complement-supplement-pair/25"},"fields":{"title":"Complement Eligibility and Supplement","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=25. Give (is a≤90?, eligible complement 90−a or none, supplement 180−a).","answer":{"kind":"expression","value":"(Yes, 65, 155)","explanation":"Guard the complementary angle with the 90° threshold; compute the supplementary angle independently using 180°. The exact result, retaining the requested order, is (Yes, 65, 155)."},"skills":["Complement Eligibility and Supplement"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0051","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"daeb71cceec770950a9fcddfaea68622e1a3b5df8365d88b9716bc41315fd558","family_id":"qf-density14-angle-pair-defects","seed":202610141051,"semantic_template":"qf-density14-angle-pair-defects/0"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=0, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-90, -180, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-90, -180, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0052","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b601eb17675d7469792d571673b91cce306424493e7e3151a2727d11e1feeee","family_id":"qf-density14-angle-pair-defects","seed":202610141052,"semantic_template":"qf-density14-angle-pair-defects/90"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=45, b=45. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(0, -90, Yes, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (0, -90, Yes, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0053","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f7c2b01c6f50ec77bc4093836fbd28d6b502c0573e7f7df06d509b223f1169e","family_id":"qf-density14-angle-pair-defects","seed":202610141053,"semantic_template":"qf-density14-angle-pair-defects/180"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=90, b=90. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(90, 0, No, Yes)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (90, 0, No, Yes)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0054","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61ad2453e10a6bfcab23b6adbc125286e0ac38ce544eb8c2041a32c474115c3d","family_id":"qf-density14-angle-pair-defects","seed":202610141054,"semantic_template":"qf-density14-angle-pair-defects/360"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=180, b=180. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(270, 180, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (270, 180, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0055","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87622ffb94e6f392f462315ad1a6b30523cecc2f683ebddb66c5ac8e623a3f82","family_id":"qf-density14-angle-pair-defects","seed":202610141055,"semantic_template":"qf-density14-angle-pair-defects/4"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=4, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-86, -176, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-86, -176, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0056","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f0e4edfe81f75aa093004eb4401dc11d345ea4361c0b0967b35c45ecea2608d6","family_id":"qf-density14-angle-pair-defects","seed":202610141056,"semantic_template":"qf-density14-angle-pair-defects/5"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=5, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-85, -175, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-85, -175, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0057","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb28fe59742840ece73917d1d2ac44f6c93b69dd4aee8d4873b00695b4f67234","family_id":"qf-density14-angle-pair-defects","seed":202610141057,"semantic_template":"qf-density14-angle-pair-defects/6"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=6, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-84, -174, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-84, -174, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0058","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ac39be97ebe203a143f5ac86d988ae72712868ea52600ce3176094f7d56cd1c","family_id":"qf-density14-angle-pair-defects","seed":202610141058,"semantic_template":"qf-density14-angle-pair-defects/7"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=7, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-83, -173, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-83, -173, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0059","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7567e856bd55fed2390386d346807cb05c9443709a95b61ee7ec636006fe51b1","family_id":"qf-density14-angle-pair-defects","seed":202610141059,"semantic_template":"qf-density14-angle-pair-defects/8"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=8, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-82, -172, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-82, -172, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0060","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"facbbf5b28cfd0e5946d8ed11abb865c7c6ff64f34d08548f8c1a8488a58532c","family_id":"qf-density14-angle-pair-defects","seed":202610141060,"semantic_template":"qf-density14-angle-pair-defects/9"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=9, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-81, -171, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-81, -171, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0061","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"94613cf8ed0c9f2ed9161d07d582d66439f22f1c019f5282be043df43aca9802","family_id":"qf-density14-angle-pair-defects","seed":202610141061,"semantic_template":"qf-density14-angle-pair-defects/10"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=10, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-80, -170, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-80, -170, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0062","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42e6fff72e9ac560c8b388cd35c0239375eda454b012d8e54538b761f4362d40","family_id":"qf-density14-angle-pair-defects","seed":202610141062,"semantic_template":"qf-density14-angle-pair-defects/11"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=11, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-79, -169, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-79, -169, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0063","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ece424b23d2c85eeedda8f0eb80cf6e7c117d7c385ea7eddf8c1275c08bb4d9","family_id":"qf-density14-angle-pair-defects","seed":202610141063,"semantic_template":"qf-density14-angle-pair-defects/12"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=12, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-78, -168, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-78, -168, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0064","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf75a4a0ff51f9a3f6422fbf5814d886e8cd49835156eda6e9a4afdf1cb1a6a9","family_id":"qf-density14-angle-pair-defects","seed":202610141064,"semantic_template":"qf-density14-angle-pair-defects/13"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=13, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-77, -167, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-77, -167, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0065","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20e1ccad29dad08842ea1e0b887d8ed47106de51341e4932c43ed2df7b3bc977","family_id":"qf-density14-angle-pair-defects","seed":202610141065,"semantic_template":"qf-density14-angle-pair-defects/14"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=14, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-76, -166, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-76, -166, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0066","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6d2e151b027c3e96e9d24f63113fdc1a29e5ce9d64f39198bd768b042957d4d","family_id":"qf-density14-angle-pair-defects","seed":202610141066,"semantic_template":"qf-density14-angle-pair-defects/15"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=15, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-75, -165, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-75, -165, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0067","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1326854d8e426b761eb7a4bada2c432843066f91a1124a436a8e41aad465b61d","family_id":"qf-density14-angle-pair-defects","seed":202610141067,"semantic_template":"qf-density14-angle-pair-defects/16"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=16, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-74, -164, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-74, -164, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0068","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1706c98ca85a2ca0f8c32d57060cc2e173a7a44c1054605421d98feb1b178f85","family_id":"qf-density14-angle-pair-defects","seed":202610141068,"semantic_template":"qf-density14-angle-pair-defects/17"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=17, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-73, -163, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-73, -163, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0069","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0e130eece9b7306dbacd6229c4ab6aca003dd1973c345ed57b90c3bc1b81daf","family_id":"qf-density14-angle-pair-defects","seed":202610141069,"semantic_template":"qf-density14-angle-pair-defects/18"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=18, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-72, -162, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-72, -162, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0070","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a6587a79aa33c10235cc50ecc100f24257bd06b9bbfa8e8385c09bd192a1cb89","family_id":"qf-density14-angle-pair-defects","seed":202610141070,"semantic_template":"qf-density14-angle-pair-defects/19"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=19, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-71, -161, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-71, -161, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0071","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e6af3759a828b79ab3e90083ea974f943b0489926d3c9e3f1d12848ffb295fa","family_id":"qf-density14-angle-pair-defects","seed":202610141071,"semantic_template":"qf-density14-angle-pair-defects/20"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=20, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-70, -160, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-70, -160, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0072","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b91cbc9cf89205e2f856bb141bb247fdc240f4ef260809c2fbf0c89b98b97c2","family_id":"qf-density14-angle-pair-defects","seed":202610141072,"semantic_template":"qf-density14-angle-pair-defects/21"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=21, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-69, -159, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-69, -159, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0073","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f138ae431f70e2fe33d313c6ea30b7c5b5beb9c41fdf7db90c750ac31fa620f","family_id":"qf-density14-angle-pair-defects","seed":202610141073,"semantic_template":"qf-density14-angle-pair-defects/22"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=22, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-68, -158, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-68, -158, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0074","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e442a043c4519bb4d005af37fa829f21aa4b8aec69b0aa42635f93c035b7f0d","family_id":"qf-density14-angle-pair-defects","seed":202610141074,"semantic_template":"qf-density14-angle-pair-defects/23"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=23, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-67, -157, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-67, -157, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0075","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6cb52d28642e4e720bb3ff641a48caa17cb5ffb65d4d460d5d197d3f354b934","family_id":"qf-density14-angle-pair-defects","seed":202610141075,"semantic_template":"qf-density14-angle-pair-defects/24"},"fields":{"title":"Two Angle-Sum Threshold Defects","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. a=24, b=0. Give (a+b−90, a+b−180, is the sum 90?, is the sum 180?).","answer":{"kind":"expression","value":"(-66, -156, No, No)","explanation":"Add the angle values, then compare the two different thresholds separately; do not infer values from a diagram. The exact result, retaining the requested order, is (-66, -156, No, No)."},"skills":["Two Angle-Sum Threshold Defects"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0076","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f02de65f27b1a2d17b6bd9b587dc90627dadd0e5f107296dc613b2950416103","family_id":"qf-density14-angle-three-part-budget","seed":202610141076,"semantic_template":"qf-density14-angle-three-part-budget/[[0,0,0],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[0, 0, 0], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([0, 0, 0], Yes, 180)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([0, 0, 0], Yes, 180)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0077","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ce74ac41c240425cda35fe3dc19e018507953fe286167f501ef5c2ce79e7d2f","family_id":"qf-density14-angle-three-part-budget","seed":202610141077,"semantic_template":"qf-density14-angle-three-part-budget/[[90,90,0],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[90, 90, 0], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([90, 180, 180], Yes, -90)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([90, 180, 180], Yes, -90)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0078","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e5951646b94fe81d793979b08077b9cf114d26b10f8b0721aa4cf151f7c9325","family_id":"qf-density14-angle-three-part-budget","seed":202610141078,"semantic_template":"qf-density14-angle-three-part-budget/[[90,90,90],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[90, 90, 90], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([90, 180, 270], No, -90)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([90, 180, 270], No, -90)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0079","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0569dba9d7bb93660d793d7d42d4a4904244d34c908ba63c8542bb3354c40980","family_id":"qf-density14-angle-three-part-budget","seed":202610141079,"semantic_template":"qf-density14-angle-three-part-budget/[[180,1,0],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[180, 1, 0], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([180, 181, 181], No, -91)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([180, 181, 181], No, -91)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0080","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7d409b1490debe58225bd8b012d57f27a79313aa68f20f0236757b2bfd463a95","family_id":"qf-density14-angle-three-part-budget","seed":202610141080,"semantic_template":"qf-density14-angle-three-part-budget/[[4,90,5],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[4, 90, 5], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([4, 94, 99], Yes, 81)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([4, 94, 99], Yes, 81)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0081","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8c3e0eb98c1a18d1608b82993508af25fd2043544a137ed86f790af983f4144","family_id":"qf-density14-angle-three-part-budget","seed":202610141081,"semantic_template":"qf-density14-angle-three-part-budget/[[5,90,6],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[5, 90, 6], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([5, 95, 101], Yes, -11)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([5, 95, 101], Yes, -11)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0082","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c958029bd1cb296a905c14831631bbbf59fa0bf2095643a9551bb734a96ecb66","family_id":"qf-density14-angle-three-part-budget","seed":202610141082,"semantic_template":"qf-density14-angle-three-part-budget/[[6,90,7],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[6, 90, 7], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([6, 96, 103], Yes, 77)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([6, 96, 103], Yes, 77)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0083","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f52f45d4dd6325286c1f9c13760cab1b8e63d7b6f43cbe2cbf0bdb137c217ce","family_id":"qf-density14-angle-three-part-budget","seed":202610141083,"semantic_template":"qf-density14-angle-three-part-budget/[[7,90,8],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[7, 90, 8], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([7, 97, 105], Yes, -15)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([7, 97, 105], Yes, -15)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0084","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b5deb7500f013e305779b0f4c1f0bc4923cb3570267212f9a11405f6d229af0b","family_id":"qf-density14-angle-three-part-budget","seed":202610141084,"semantic_template":"qf-density14-angle-three-part-budget/[[8,90,9],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[8, 90, 9], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([8, 98, 107], Yes, 73)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([8, 98, 107], Yes, 73)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0085","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4345aea5b5fa4111904518be3c4e9848c2032c20296787ac32525de1489ab1b5","family_id":"qf-density14-angle-three-part-budget","seed":202610141085,"semantic_template":"qf-density14-angle-three-part-budget/[[9,90,10],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[9, 90, 10], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([9, 99, 109], Yes, -19)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([9, 99, 109], Yes, -19)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0086","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07f0c0781899df6886a84fe06f6d4e81e9795d8daeea6167e4cb7f2969c4f57a","family_id":"qf-density14-angle-three-part-budget","seed":202610141086,"semantic_template":"qf-density14-angle-three-part-budget/[[10,90,11],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[10, 90, 11], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([10, 100, 111], Yes, 69)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([10, 100, 111], Yes, 69)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0087","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5da6555198d35f2f127f34c81d15549b7b95dcf12ee72174b168c9ecff9de131","family_id":"qf-density14-angle-three-part-budget","seed":202610141087,"semantic_template":"qf-density14-angle-three-part-budget/[[11,90,12],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[11, 90, 12], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([11, 101, 113], Yes, -23)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([11, 101, 113], Yes, -23)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0088","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4c878a451ae4fe514505de002da83f4ffd73ffdad9b309d4ce9ccdb8572558e","family_id":"qf-density14-angle-three-part-budget","seed":202610141088,"semantic_template":"qf-density14-angle-three-part-budget/[[12,90,13],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[12, 90, 13], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([12, 102, 115], Yes, 65)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([12, 102, 115], Yes, 65)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0089","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"294b13236c18c401393c8c01b9fe9c00d07c0783092b30fb13e4028ee2d212e2","family_id":"qf-density14-angle-three-part-budget","seed":202610141089,"semantic_template":"qf-density14-angle-three-part-budget/[[13,90,14],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[13, 90, 14], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([13, 103, 117], Yes, -27)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([13, 103, 117], Yes, -27)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0090","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f0cda32834a98ee8d6aa584d72aec1ee4b726fffc475440b8b0dc0ceefde0aac","family_id":"qf-density14-angle-three-part-budget","seed":202610141090,"semantic_template":"qf-density14-angle-three-part-budget/[[14,90,15],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[14, 90, 15], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([14, 104, 119], Yes, 61)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([14, 104, 119], Yes, 61)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0091","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"829460855769c2d31583cf60612fb97bf82a14b91f08c21bfc48f454f0bbba22","family_id":"qf-density14-angle-three-part-budget","seed":202610141091,"semantic_template":"qf-density14-angle-three-part-budget/[[15,90,16],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[15, 90, 16], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([15, 105, 121], Yes, -31)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([15, 105, 121], Yes, -31)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0092","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d34d32bd141fb2cb0c84f2ebe7afa1af2804ac6941637fd8d5fb57a3a95ff806","family_id":"qf-density14-angle-three-part-budget","seed":202610141092,"semantic_template":"qf-density14-angle-three-part-budget/[[16,90,17],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[16, 90, 17], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([16, 106, 123], Yes, 57)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([16, 106, 123], Yes, 57)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0093","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"46ceddde7a7db45388178edfc8b9a6ba32c4e3681978ef9dd832cc843748c800","family_id":"qf-density14-angle-three-part-budget","seed":202610141093,"semantic_template":"qf-density14-angle-three-part-budget/[[17,90,18],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[17, 90, 18], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([17, 107, 125], Yes, -35)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([17, 107, 125], Yes, -35)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0094","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe232c1704a3f14244e69be920071fb583ce811e1010ee0bb851106aec8def3d","family_id":"qf-density14-angle-three-part-budget","seed":202610141094,"semantic_template":"qf-density14-angle-three-part-budget/[[18,90,19],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[18, 90, 19], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([18, 108, 127], Yes, 53)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([18, 108, 127], Yes, 53)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0095","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2347188187025b2e3e6006f4500019ceaa2bf9dfa0b8d65f94396542e6250de1","family_id":"qf-density14-angle-three-part-budget","seed":202610141095,"semantic_template":"qf-density14-angle-three-part-budget/[[19,90,20],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[19, 90, 20], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([19, 109, 129], Yes, -39)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([19, 109, 129], Yes, -39)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0096","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e35a1cfffab540c34027cb7e74d279fe43e849f90b07ad3a1badec2a6c492388","family_id":"qf-density14-angle-three-part-budget","seed":202610141096,"semantic_template":"qf-density14-angle-three-part-budget/[[20,90,21],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[20, 90, 21], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([20, 110, 131], Yes, 49)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([20, 110, 131], Yes, 49)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0097","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e3e36e745a417acbc573a094a59bdb293f19f037a742fe2e0325e5fe30ddaf8","family_id":"qf-density14-angle-three-part-budget","seed":202610141097,"semantic_template":"qf-density14-angle-three-part-budget/[[21,90,22],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[21, 90, 22], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([21, 111, 133], Yes, -43)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([21, 111, 133], Yes, -43)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0098","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"186a2b9d640ce7209a6e50190b1752a3092a0a7e9a78acea3c581444913d255e","family_id":"qf-density14-angle-three-part-budget","seed":202610141098,"semantic_template":"qf-density14-angle-three-part-budget/[[22,90,23],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[22, 90, 23], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([22, 112, 135], Yes, 45)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([22, 112, 135], Yes, 45)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0099","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc94ce6a8d9fce1c13faff7b5a32d8da28d5595dcf310bba3a8d844f7ec0af06","family_id":"qf-density14-angle-three-part-budget","seed":202610141099,"semantic_template":"qf-density14-angle-three-part-budget/[[23,90,24],90]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[23, 90, 24], target=90. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([23, 113, 137], Yes, -47)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([23, 113, 137], Yes, -47)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261010-advance-20261014-r01-angle-0100","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"987c0634de084ba5c4c91c081213aa30be87ac9051476c7dc9a02e2ac5224bec","family_id":"qf-density14-angle-three-part-budget","seed":202610141100,"semantic_template":"qf-density14-angle-three-part-budget/[[24,90,25],180]"},"fields":{"title":"Three-Part Prefix Budget and Eligibility","stem":"Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. Ordered parts=[24, 90, 25], target=180. Give (three prefix sums, is the total≤180?, target−total).","answer":{"kind":"expression","value":"([24, 114, 139], Yes, 41)","explanation":"Accumulate in the original order without taking a modulus; a total above 180 is not an angle in this entry’s nondirected slice. The exact result, retaining the requested order, is ([24, 114, 139], Yes, 41)."},"skills":["Three-Part Prefix Budget and Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}