find the measure of the angle or arc.

$m\widehat{pq} = $

$m\angle pqr = $

Question

find the measure of the angle or arc.

$m\widehat{pq} = $

$m\angle pqr = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arc Measure in Circles" ], "new_concepts": [ "Tangent-Secant Angle Theorem" ], "current_concepts": [ "Arc Measure in Circles", "Tangent-Secant Angle Theorem" ] } ## Calculate the measure of arc PQ $$ \begin{aligned} m\widehat{PQ} &= 360^\circ - 276^\circ \ m\widehat{PQ} &= 84^\circ \end{aligned} $$ ## Calculate the measure of angle PQR $$ \begin{aligned} m\angle PQR &= \frac{1}{2} \cdot m\widehat{PQ} \ m\angle PQR &= \frac{1}{2} \cdot 84^\circ \ m\angle PQR &= 42^\circ \end{aligned} $$ Find the measure of the angle or arc. $m\widehat{PQ} =$ $84$$^\circ$ $m\angle PQR =$ $42$$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Secant Angle Theorem" ] }

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Question

Explanation:

Calculate the measure of arc PQ

Calculate the measure of angle PQR

Answer: