the circle below has center $d$. suppose that $m \angle bac = 46^{\circ}$. find the following.

(a) $m \widehat{bc} = \box^{\circ}$
(b) $m \angle bdc = \box^{\circ}$

Question

the circle below has center $d$. suppose that $m \angle bac = 46^{\circ}$. find the following.

(a) $m \widehat{bc} = \box^{\circ}$
(b) $m \angle bdc = \box^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Inscribed Angle Theorem", "Central Angle" ], "new_concepts": [], "current_concepts": [ "Inscribed Angle Theorem", "Central Angle", "Arc Measure" ] } ## Identify the given information We are given a circle with center $D$. An inscribed angle $\angle BAC$ has a measure of $46^\circ$. We need to find the measure of the intercepted arc $\widehat{BC}$ and the measure of the central angle $\angle BDC$. ## Find the measure of arc BC Using the **Inscribed Angle Theorem** knowledge point $$ \begin{aligned} m\widehat{BC} &= 2 \cdot m\angle BAC \ m\widehat{BC} &= 2 \cdot 46^\circ = 92^\circ \end{aligned} $$ ## Find the measure of angle BDC Using the **Central Angle** knowledge point $$ \begin{aligned} m\angle BDC &= m\widehat{BC} \ m\angle BDC &= 92^\circ \end{aligned} $$ ## Question 1 (a) $m\widehat{BC} = 92^\circ$ ## Question 2 (b) $m\angle BDC = 92^\circ$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Angle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given information

Find the measure of arc BC

Find the measure of angle BDC

Answer:

Question 1

Question 2