# Question 1217: Classifying an Explicit 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.

R0001-01217 · q-20260922-angle-degree-classification-0017



## Original question and givens

Angle θ has the explicitly stated integer measure 137°. Without inferring from a drawing, is θ acute, right, obtuse, or straight?


- G001 — Angle θ has the explicitly stated integer measure 137°. Without inferring from a drawing, is θ acute, right, obtuse, or straight?





## 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=137°

After

acute:0<θ<90; right:θ=90; obtuse:90<θ<180; straight:θ=180

Conditions: none

The four disjoint cases cover the full declared angle range.

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





S003 · calculationBefore

θ−90 := sub(137, 90)

After

θ−90 = 47

Conditions: none

Check position relative to90, then the180-degree endpoint.

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





S004 · impliesBefore

θ=137°; θ−90=47

After

category=obtuse angle

Conditions: none

Use strict boundaries and equality to select one case; do not place90 or180 in the wrong open interval.

Step identifiers and dependenciesRule: angle_case_selection · 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 — Recompute θ−90 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

obtuse angle

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: 77f61f36af6d7e76eb412b8a9c0a3a3b585f329cf42bcd26e500e855634c8591
- candidate record SHA-256: 18578c4ac9202a2d2ce83ad53ffa54789e04c1bb99a4391e6e633b974bfe4d1b
- 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-degree-classification-0017.json)