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R0010-05809 · q-20261008-advance-20261012-r05-right-triangle-0009
Exact degrees: a nondegenerate plane triangle has γ=90° and α=10°. Give (β in degrees, α+β in degrees).
G001 — Exact degrees: a nondegenerate plane triangle has γ=90° and α=10°. Give (β in degrees, α+β in degrees).Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
angle unit=degrees;exact declared protocol
After
check qualifications before geometric conclusions;no tolerance
Conditions: none
Use the declared exact angle protocol,not a sketch or floating tolerance.Candidate angle data do not by themselves construct a triangle.
Rule: exact_right_angle_protocol · Uses: G001
Before
acute-angle budget := sub(180, 90)
After
acute-angle budget = 90
Conditions: none
Under the supplied nondegenerate Euclidean plane-triangle premises,the180-degree sum minus the90-degree right angle leaves90 for the two acute angles.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
other acute angle beta := sub(90, 10)
After
other acute angle beta = 80
Conditions: none
Subtract the supplied α from the two-acute-angle budget.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
alpha plus beta := sum(10, 80)
After
alpha plus beta = 90
Conditions: none
Add back to audit the acute-angle sum,retaining the requested field order.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
1≤α=10≤89;β=80
After
α+β=90;both acute
Conditions: none
The strict acute range for α also places β between1 and89 degrees.This derives values under the given right-triangle premises,not a construction proof.
Rule: right_triangle_remainder_premises · Uses: G001, S004
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Recompute alpha plus beta with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute other acute angle beta with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute acute-angle budget with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(80, 90)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
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