if $\angle def$ measures $60^\circ$, what is the measure of $\widehat{df}$?

a. $300^\circ$
b. $120^\circ$
c. $30^\circ$
d. $60^\circ$

Question

if $\angle def$ measures $60^\circ$, what is the measure of $\widehat{df}$?

a. $300^\circ$
b. $120^\circ$
c. $30^\circ$
d. $60^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Definition", "Minor Arc" ], "new_concepts": [ "Central Angle Theorem" ], "current_concepts": [ "Circle Definition", "Minor Arc", "Central Angle Theorem" ] } ## Identify the angle type and given measure $$ \begin{aligned} &\text{Central Angle: } \angle DEF \ &m\angle DEF = 60^\circ \end{aligned} $$ ## Apply the central angle theorem $$ \begin{aligned} &m\widehat{DF} = m\angle DEF \ &m\widehat{DF} = 60^\circ \end{aligned} $$

A. $300^\circ$

B. $120^\circ$

C. $30^\circ$

D. $60^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Central Angle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the angle type and given measure

Apply the central angle theorem

Answer: