Question 1249: Complementary Angle Measure

Original question and givens

Angle θ has the explicitly stated measure 77°. Find an integer-degree measure complementary to θ; adjacency is not required and no value is inferred from a diagram.

• G001 — Angle θ has the explicitly stated measure 77°. Find an integer-degree measure complementary to θ; adjacency is not required and no value is inferred from a diagram.

Definition and scope

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.

• mko-angle

Step-by-step derivation

angle measurements are explicit integers in degrees

classification uses values, not diagram appearance

θ=77°; required sum=90°

θ+φ=90°

φ := sub(90, 77)

φ = 13

θ+φ := sum(77, 13)

θ+φ = 90

0<77<90

0<13<90; answer=13°

Reverse checks

• 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 θ+φ with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute φ with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

13°

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.