find the measure of the arc.
$m\widehat{lk} = \square^{\circ}$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Angles Inside Circle Theorem" ], "current_concepts": [ "Angles Inside Circle Theorem", "Arc Measure" ] } ## Apply the Angles Inside Circle Theorem $$ \angle KJL = \frac{1}{2} (m\widehat{GM} + m\widehat{LK}) $$ ## Substitute the given values $$ 58^\circ = \frac{1}{2} (52^\circ + m\widehat{LK}) $$ ## Solve for the arc measure $$ \begin{aligned} 116^\circ &= 52^\circ + m\widehat{LK} \ m\widehat{LK} &= 64^\circ \end{aligned} $$ Find the measure of the arc. $m\widehat{LK} =$ 64$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Inside Circle Theorem" ] }

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Question

Explanation:

Apply the Angles Inside Circle Theorem

Substitute the given values

Solve for the arc measure

Answer: