g.gsr.8.1 (mc)

$\angle bdc = 70^\circ$ on circle a. find the measure of $\widehat{bc}$.

Question

g.gsr.8.1 (mc)

$\angle bdc = 70^\circ$ on circle a. find the measure of $\widehat{bc}$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Angle", "Arc Measure" ], "new_concepts": [], "current_concepts": [ "Inscribed Angle", "Arc Measure" ] } ## Identify the given angle and its intercepted arc $$ \begin{aligned} &\angle BDC = 70^\circ \quad (\text{Inscribed angle on Circle } A) \ &\text{Intercepted Arc} = \widehat{BC} \end{aligned} $$ ## Apply the Inscribed Angle Theorem $$ \begin{aligned} &m\angle BDC = \frac{1}{2} \cdot m\widehat{BC} \ &70^\circ = \frac{1}{2} \cdot m\widehat{BC} \end{aligned} $$ ## Solve for the measure of the arc $$ \begin{aligned} &m\widehat{BC} = 2 \cdot 70^\circ \ &m\widehat{BC} = 140^\circ \end{aligned} $$ $140^\circ$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Angle" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given angle and its intercepted arc

Apply the Inscribed Angle Theorem

Solve for the measure of the arc

Answer: