Question 1286: Relation Between Two Explicit Angle Measures

Original question and givens

Angles α=40° and β=50° have explicitly stated integer measures. Using only α+β, are they complementary, supplementary, or neither?

• G001 — Angles α=40° and β=50° have explicitly stated integer measures. Using only α+β, are they complementary, supplementary, or neither?

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

α+β := sum(40, 50)

α+β = 90

sum=90°

complementary iff sum90°; supplementary iff sum180°

α+β=90°

relation=complementary

Reverse checks

• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Recompute α+β 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.

Result

complementary

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.