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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": [], "new_concepts": [ "Angles Inside Circles", "Intersecting Chords Theorem" ], "current_concepts": [ "Angles Inside Circles", "Intersecting Chords Theorem", "Arc Measure" ] } ## Identify the given values and geometric relationship $$ \begin{aligned} &\text{Chords } KM \text{ and } LJ \text{ intersect at point } A \text{ inside circle } O.\ &m\widehat{KJ} = 170^\circ\ &m\widehat{LM} = 80^\circ \end{aligned} $$ ## Apply the intersecting chords angle theorem $$ \begin{aligned} m\angle MAJ &= \frac{1}{2}(m\widehat{KJ} + m\widehat{LM})\ m\angle MAJ &= \frac{1}{2}(170^\circ + 80^\circ) \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} m\angle MAJ &= \frac{1}{2}(250^\circ) = 125^\circ \end{aligned} $$

(A) 50°

(B) 55°

(C) 125°

(D) 250°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Angles Inside Circles" ] }

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Question

Explanation:

Identify the given values and geometric relationship

Apply the intersecting chords angle theorem

Calculate the final angle measure

Answer: