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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Inscribed Angle Theorem", "Circle Geometry" ] } ## Identify the given values and the geometric relationship $$ \begin{aligned} &\text{Arc } AB = 76^\circ \ &\angle C \text{ is an inscribed angle intercepting arc } AB \end{aligned} $$ ## Apply the Inscribed Angle Theorem $$ \begin{aligned} &m\angle C = \frac{1}{2} \cdot m(\text{arc } AB) \ &m\angle C = \frac{1}{2} \cdot 76^\circ = 38^\circ \end{aligned} $$

(A) $38^\circ$

(B) $76^\circ$

(C) $90^\circ$

(D) $152^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Angle Theorem" ] }

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Explanation:

Identify the given values and the geometric relationship

Apply the Inscribed Angle Theorem

Answer: