what is $m\angle lnm$?

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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": [ "Angles Inside Circle Theorem" ], "new_concepts": [], "current_concepts": [ "Angles Inside Circle Theorem" ] } ## Identify the given arc measures and target angle $$ \begin{aligned} &m\widehat{LM} = 155^\circ\ &m\widehat{KT} = 65^\circ\ &\text{Target angle: } m\angle LNM \end{aligned} $$ ## Apply the Angles Inside Circle Theorem $$ \begin{aligned} &m\angle LNM = \frac{1}{2}(m\widehat{LM} + m\widehat{KT})\ &m\angle LNM = \frac{1}{2}(155^\circ + 65^\circ) \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} &m\angle LNM = \frac{1}{2}(220^\circ) = 110^\circ \end{aligned} $$ What is $m\angle LNM$? 110$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Inside Circle Theorem" ] }

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Question

Explanation:

Identify the given arc measures and target angle

Apply the Angles Inside Circle Theorem

Calculate the final angle measure

Answer: