find the measure of each angle or arc.

$m\angle gfe = $ $^{\circ}$

$m\widehat{ef} = $ $^{\circ}$

$m\widehat{gf} = $ $^{\circ}$

Question

find the measure of each angle or arc.

$m\angle gfe = $  $^{\circ}$

$m\widehat{ef} = $  $^{\circ}$

$m\widehat{gf} = $  $^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Isosceles Triangle Properties" ], "new_concepts": [ "Congruent Chords and Arcs", "Inscribed Angle Theorem" ], "current_concepts": [ "Isosceles Triangle Properties", "Congruent Chords and Arcs", "Inscribed Angle Theorem" ] } ## Calculate the measures of the congruent chords and arcs $$ \begin{aligned} &EF = GF \implies m\overparen{EF} = m\overparen{GF} \ &m\overparen{EG} = 78^\circ \ &m\overparen{EF} + m\overparen{GF} + m\overparen{EG} = 360^\circ \ &2 \cdot m\overparen{GF} + 78^\circ = 360^\circ \ &2 \cdot m\overparen{GF} = 282^\circ \ &m\overparen{GF} = 141^\circ \ &m\overparen{EF} = 141^\circ \end{aligned} $$ ## Calculate the inscribed angle measure $$ \begin{aligned} &m\angle GFE = \frac{1}{2} \cdot m\overparen{EG} \ &m\angle GFE = \frac{1}{2} \cdot 78^\circ = 39^\circ \end{aligned} $$ Find the measure of each angle or arc. $m\angle GFE =$ 39$^\circ$ $m\overparen{EF} =$ 141$^\circ$ $m\overparen{GF} =$ 141$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Angle Theorem" ] }

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Question

Explanation:

Calculate the measures of the congruent chords and arcs

Calculate the inscribed angle measure

Answer: