find the measure of each angle or arc.

$m \angle lmn = $

$m\widehat{mn} = $

$m\widehat{ln} = $

Question

find the measure of each angle or arc.

$m \angle lmn = $

$m\widehat{mn} = $

$m\widehat{ln} = $

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": [ "Inscribed Quadrilateral Theorem" ], "current_concepts": [ "Inscribed Quadrilateral Theorem", "Inscribed Angle Theorem" ] } ## Find the measure of angle LMN $$ \begin{aligned} m\angle LMN + m\angle LZN &= 180^\circ \ m\angle LMN + 104^\circ &= 180^\circ \ m\angle LMN &= 76^\circ \end{aligned} $$ ## Find the measure of arc MN $$ \begin{aligned} m\widehat{LMN} &= 2 \cdot m\angle LZN = 2 \cdot 104^\circ = 208^\circ \ m\widehat{MN} &= m\widehat{LMN} - m\widehat{LM} \ m\widehat{MN} &= 208^\circ - 140^\circ = 68^\circ \end{aligned} $$ ## Find the measure of arc LN $$ \begin{aligned} m\widehat{LN} &= 2 \cdot m\angle LMN \ m\widehat{LN} &= 2 \cdot 76^\circ = 152^\circ \end{aligned} $$ Find the measure of each angle or arc. $m\angle LMN =$ 76$^\circ$ $m\widehat{MN} =$ 68$^\circ$ $m\widehat{LN} =$ 152$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Quadrilateral Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Find the measure of angle LMN

Find the measure of arc MN

Find the measure of arc LN

Answer: