# Exact Angle Qualification and Labeled Right Vertices This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed. This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately. batch-20261008-advance-20261012-r05-right-triangle-foundations · 2026-10-08 · 100 questions This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt. ## 1. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=1°. Give (β in degrees, α+β in degrees). View answer and explanation(89, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (89, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0001/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 2. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=89°. Give (β in degrees, α+β in degrees). View answer and explanation(1, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (1, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0002/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 3. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=45°. Give (β in degrees, α+β in degrees). View answer and explanation(45, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (45, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0003/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 4. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=5°. Give (β in degrees, α+β in degrees). View answer and explanation(85, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (85, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0004/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 5. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=6°. Give (β in degrees, α+β in degrees). View answer and explanation(84, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (84, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0005/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 6. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=7°. Give (β in degrees, α+β in degrees). View answer and explanation(83, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (83, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0006/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 7. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=8°. Give (β in degrees, α+β in degrees). View answer and explanation(82, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (82, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0007/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 8. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=9°. Give (β in degrees, α+β in degrees). View answer and explanation(81, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (81, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0008/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 9. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=10°. Give (β in degrees, α+β in degrees). View answer and explanation(80, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (80, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0009/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 10. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=11°. Give (β in degrees, α+β in degrees). View answer and explanation(79, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (79, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0010/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 11. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=12°. Give (β in degrees, α+β in degrees). View answer and explanation(78, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (78, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0011/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 12. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=13°. Give (β in degrees, α+β in degrees). View answer and explanation(77, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (77, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0012/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 13. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=14°. Give (β in degrees, α+β in degrees). View answer and explanation(76, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (76, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0013/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 14. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=15°. Give (β in degrees, α+β in degrees). View answer and explanation(75, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (75, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0014/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 15. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=16°. Give (β in degrees, α+β in degrees). View answer and explanation(74, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (74, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0015/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 16. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=17°. Give (β in degrees, α+β in degrees). View answer and explanation(73, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (73, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0016/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 17. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=18°. Give (β in degrees, α+β in degrees). View answer and explanation(72, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (72, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0017/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 18. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=19°. Give (β in degrees, α+β in degrees). View answer and explanation(71, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (71, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0018/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 19. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=20°. Give (β in degrees, α+β in degrees). View answer and explanation(70, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (70, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0019/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 20. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=21°. Give (β in degrees, α+β in degrees). View answer and explanation(69, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (69, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0020/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 21. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=22°. Give (β in degrees, α+β in degrees). View answer and explanation(68, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (68, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0021/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 22. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=23°. Give (β in degrees, α+β in degrees). View answer and explanation(67, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (67, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0022/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 23. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=24°. Give (β in degrees, α+β in degrees). View answer and explanation(66, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (66, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0023/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 24. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=25°. Give (β in degrees, α+β in degrees). View answer and explanation(65, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (65, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0024/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 25. Acute-Angle Remainder in a Given Right Triangle Exact degrees: a nondegenerate plane triangle has γ=90° and α=26°. Give (β in degrees, α+β in degrees). View answer and explanation(64, 90) Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (64, 90). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0025/) Right triangle · qf-density12-right-triangle-angle-remainder · candidate ## 26. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 90, 0]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(No, No, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0026/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 27. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[60, 60, 60]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, No, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, No, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0027/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 28. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 30, 60]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0028/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 29. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[-1, 90, 91]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(No, No, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0029/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 30. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 45, 46]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(No, No, 1) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 1). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0030/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 31. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[0, 0, 180]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(No, No, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0031/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 32. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 7, 83]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0032/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 33. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 8, 82]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0033/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 34. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 9, 81]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0034/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 35. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 10, 80]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0035/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 36. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 11, 79]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0036/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 37. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 12, 78]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0037/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 38. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 13, 77]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0038/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 39. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 14, 76]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0039/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 40. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 15, 75]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0040/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 41. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 16, 74]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0041/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 42. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 17, 73]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0042/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 43. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 18, 72]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0043/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 44. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 19, 71]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0044/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 45. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 20, 70]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0045/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 46. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 21, 69]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0046/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 47. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 22, 68]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0047/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 48. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 23, 67]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0048/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 49. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 24, 66]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0049/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 50. Candidate Triangle-Angle Qualification Exact-degree candidate angles=[90, 25, 65]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180). View answer and explanation(Yes, Yes, 0) Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0050/) Right triangle · qf-density12-right-triangle-validity-pair · candidate ## 51. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 45, 45], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [45, 45]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [45, 45]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0051/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 52. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[1, 90, 89], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [1, 89]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [1, 89]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0052/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 53. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[3, 87, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [3, 87]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [3, 87]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0053/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 54. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 4, 86], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [4, 86]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [4, 86]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0054/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 55. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[5, 90, 85], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [5, 85]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [5, 85]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0055/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 56. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[6, 84, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [6, 84]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [6, 84]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0056/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 57. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 7, 83], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [7, 83]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [7, 83]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0057/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 58. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[8, 90, 82], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [8, 82]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [8, 82]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0058/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 59. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[9, 81, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [9, 81]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [9, 81]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0059/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 60. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 10, 80], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [10, 80]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [10, 80]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0060/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 61. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[11, 90, 79], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [11, 79]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [11, 79]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0061/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 62. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[12, 78, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [12, 78]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [12, 78]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0062/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 63. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 13, 77], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [13, 77]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [13, 77]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0063/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 64. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[14, 90, 76], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [14, 76]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [14, 76]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0064/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 65. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[15, 75, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [15, 75]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [15, 75]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0065/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 66. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 16, 74], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [16, 74]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [16, 74]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0066/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 67. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[17, 90, 73], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [17, 73]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [17, 73]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0067/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 68. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[18, 72, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [18, 72]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [18, 72]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0068/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 69. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 19, 71], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [19, 71]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [19, 71]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0069/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 70. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[20, 90, 70], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [20, 70]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [20, 70]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0070/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 71. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[21, 69, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [21, 69]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [21, 69]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0071/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 72. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 22, 68], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [22, 68]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [22, 68]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0072/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 73. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[23, 90, 67], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(2, [1, 3], [23, 67]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [23, 67]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0073/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 74. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[24, 66, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(3, [1, 2], [24, 66]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [24, 66]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0074/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 75. Labeled Right Vertex and Opposite Side Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 25, 65], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles). View answer and explanation(1, [2, 3], [25, 65]) Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [25, 65]). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0075/) Right triangle · qf-density12-right-triangle-marked-vertices · candidate ## 76. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(1/2)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(90/1, Yes) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (90/1, Yes). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0076/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 77. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(5/2)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(450/1, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (450/1, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0077/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 78. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(0/1)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(0/1, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (0/1, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0078/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 79. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(-1/2)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(-90/1, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (-90/1, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0079/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 80. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(1/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(180/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (180/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0080/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 81. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(2/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(360/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (360/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0081/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 82. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(3/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(540/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (540/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0082/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 83. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(4/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(720/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (720/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0083/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 84. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(5/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(900/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (900/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0084/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 85. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(6/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(1080/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1080/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0085/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 86. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(7/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(180/1, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (180/1, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0086/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 87. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(8/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(1440/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1440/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0087/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 88. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(9/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(1620/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1620/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0088/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 89. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(10/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(1800/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1800/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0089/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 90. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(11/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(1980/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1980/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0090/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 91. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(12/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(2160/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2160/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0091/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 92. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(13/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(2340/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2340/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0092/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 93. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(14/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(360/1, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (360/1, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0093/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 94. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(15/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(2700/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2700/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0094/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 95. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(16/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(2880/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2880/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0095/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 96. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(17/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(3060/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3060/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0096/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 97. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(18/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(3240/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3240/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0097/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 98. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(19/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(3420/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3420/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0098/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 99. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(20/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(3600/7, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3600/7, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0099/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate ## 100. Exact π-Multiple Candidate without Periodic Wrapping Candidate θ=(21/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period. View answer and explanation(540/1, No) Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (540/1, No). [Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r05-right-triangle-0100/) Right triangle · qf-density12-right-triangle-pi-multiple · candidate [Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261008-advance-20261012-r05-right-triangle-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261008-advance-20261012-r05-right-triangle-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261008-advance-20261012-r05-right-triangle-foundations/validation-report.json)