find the measure of each angle or arc.
$m\widehat{lk} = $
$m\widehat{lkj} = $
$m\angle klj = $
$m\angle ljk = $

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Angle Theorem" ], "new_concepts": [ "Arc Addition Postulate" ], "current_concepts": [ "Inscribed Angle Theorem", "Arc Addition Postulate" ] } ## Calculate the measure of arc LK $$ \begin{aligned} m\widehat{LK} &= 360^\circ - m\widehat{LJ} - m\widehat{JK} \ m\widehat{LK} &= 360^\circ - 100^\circ - 140^\circ = 120^\circ \end{aligned} $$ ## Calculate the measure of arc LKJ $$ \begin{aligned} m\widehat{LKJ} &= m\widehat{LK} + m\widehat{KJ} \ m\widehat{LKJ} &= 120^\circ + 140^\circ = 260^\circ \end{aligned} $$ ## Calculate the measures of angles KLJ and LJK $$ \begin{aligned} m\angle KLJ &= \frac{1}{2} \cdot m\widehat{KJ} = \frac{1}{2} \cdot 140^\circ = 70^\circ \ m\angle LJK &= \frac{1}{2} \cdot m\widehat{LK} = \frac{1}{2} \cdot 120^\circ = 60^\circ \end{aligned} $$ Find the measure of each angle or arc. $m\widehat{LK} =$ 120$^\circ$ $m\widehat{LKJ} =$ 260$^\circ$ $m\angle KLJ =$ 70$^\circ$ $m\angle LJK =$ 60$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Angle Theorem" ] }

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Explanation:

Calculate the measure of arc LK

Calculate the measure of arc LKJ

Calculate the measures of angles KLJ and LJK

Answer: