what is the measure of arc qr?

$26^\circ$
$52^\circ$
$104^\circ$
$128^\circ$

Question

what is the measure of arc qr?

$26^\circ$
$52^\circ$
$104^\circ$
$128^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Inscribed Angle Theorem", "Circle Geometry" ] } ## Identify the inscribed angle and its intercepted arc $$ \begin{aligned} &\angle QSR = 52^\circ\ &\text{Intercepted Arc} = \text{arc } QR \end{aligned} $$ ## Apply the Inscribed Angle Theorem $$ \begin{aligned} &m\angle QSR = \frac{1}{2} \cdot m(\text{arc } QR)\ &52^\circ = \frac{1}{2} \cdot m(\text{arc } QR) \end{aligned} $$ ## Solve for the measure of arc QR $$ \begin{aligned} &m(\text{arc } QR) = 2 \cdot 52^\circ = 104^\circ \end{aligned} $$

(A) $26^\circ$

(B) $52^\circ$

(C) $104^\circ$

(D) $128^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the inscribed angle and its intercepted arc

Apply the Inscribed Angle Theorem

Solve for the measure of arc QR

Answer: