# Question 1294: Relation Between Two Explicit Angle Measures

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0001-01294 · q-20260922-angle-pair-relation-0019



## Original question and givens

Angles α=120° and β=30° have explicitly stated integer measures. Using only α+β, are they complementary, supplementary, or neither?


- G001 — Angles α=120° and β=30° 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](https://ocme.evemisslab.com/en/mko/mko-angle/)





## Step-by-step derivation

S001 · impliesBefore

angle measurements are explicit integers in degrees

After

classification uses values, not diagram appearance

Conditions: none

Retain degree units and the declared range rather than estimating from a diagram.

Step identifiers and dependenciesRule: degree_measure_domain · Uses: G001





S002 · calculationBefore

α+β := sum(120, 30)

After

α+β = 150

Conditions: none

Add the two explicit degree measures; order does not affect the sum.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001





S003 · impliesBefore

sum=150°

After

complementary iff sum90°; supplementary iff sum180°

Conditions: none

The relation depends on their sum; adjacency is not required.

Step identifiers and dependenciesRule: angle_pair_definitions · Uses: G001, S002





S004 · impliesBefore

α+β=150°

After

relation=neither

Conditions: none

If the sum is neither90 nor180, neither relation holds.

Step identifiers and dependenciesRule: angle_pair_verdict · Uses: G001, S003









## 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

neither

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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: 09313924f286ff87332e2e26e2c5d04de395217151497dd742382a3276c18927
- candidate record SHA-256: f0d4a80117ede51ff18ec7626ede217fa96cd2566a3c8f8136b8ae5fb4731231
- semantic review receipt SHA-256: c3b44ce8ed60ada6902fb206627537d5f90ba2a867eaba43a36f903280c496cc
- question-first witness SHA-256: 3e91602adc7f81a2671a2a3ffaf6a447028b56abc5853e8271673d76f30cd7ad
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260922-angle-pair-relation-0019.json)