# Question 1256: Supplementary Angle Measure

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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.

R0001-01256 · q-20260922-angle-supplement-measure-0006



## Original question and givens

Angle θ has the explicitly stated measure 33°. Find an integer-degree measure supplementary to θ; adjacency is not required and no value is inferred from a diagram.


- G001 — Angle θ has the explicitly stated measure 33°. Find an integer-degree measure supplementary 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](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 · impliesBefore

θ=33°; required sum=180°

After

θ+φ=180°

Conditions: none

Express the complementary or supplementary definition as an equation first.

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





S003 · calculationBefore

φ := sub(180, 33)

After

φ = 147

Conditions: none

Subtract the original angle from the target sum.

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





S004 · calculationBefore

θ+φ := sum(33, 147)

After

θ+φ = 180

Conditions: none

Add back to verify the required total measure.

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





S005 · impliesBefore

0<33<180

After

0<147<180; answer=147°

Conditions: none

The result is positive and retains degree units; no adjacency or collinearity assumption is added.

Step identifiers and dependenciesRule: positive_degree_result · Uses: G001, S004









## 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

147°

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: bfad929bae9492cbfd17ac50c0cb2a5fdc933c43a16e61708d4772b36771ee92
- candidate record SHA-256: 20e9877248edd19942132e50970410a46416532f6074dea385fe0b0067c85396
- 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-supplement-measure-0006.json)