in circle d, $\angle edh \cong \angle edg$.
what is the measure of $\widehat{eh}$?

$114^\circ$
$123^\circ$
$228^\circ$
$246^\circ$

Question

in circle d, $\angle edh \cong \angle edg$.
what is the measure of $\widehat{eh}$?

$114^\circ$
$123^\circ$
$228^\circ$
$246^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Central Angle Theorem", "Congruent Arcs", "Circle Geometry" ], "current_concepts": [ "Central Angle Theorem", "Congruent Arcs", "Circle Geometry" ] } ## Determine the measure of central angle $\angle EDG$ $$ \begin{aligned} m\widehat{EF} &= 57^\circ \ m\widehat{FG} &= 66^\circ \ m\widehat{EG} &= m\widehat{EF} + m\widehat{FG} = 57^\circ + 66^\circ = 123^\circ \ m\angle EDG &= m\widehat{EG} = 123^\circ \end{aligned} $$ ## Find the measure of central angle $\angle EDH$ $$ \begin{aligned} \angle EDH &\cong \angle EDG \ m\angle EDH &= m\angle EDG = 123^\circ \end{aligned} $$ ## Calculate the measure of arc $\widehat{EH}$ $$ m\widehat{EH} = m\angle EDH = 123^\circ $$

114°

123°

228°

246°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the measure of central angle \(\angle EDG\)

Find the measure of central angle \(\angle EDH\)

Calculate the measure of arc \(\widehat{EH}\)

Answer: