circumscribed angle theorem practice

angle $a$ is circumscribed about circle $o$.

what is the measure of $\angle a$?

Question

circumscribed angle theorem practice

angle $a$ is circumscribed about circle $o$.

what is the measure of $\angle a$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent Line to Circle", "Quadrilateral Angle Sum" ], "new_concepts": [], "current_concepts": [ "Tangent Line to Circle", "Quadrilateral Angle Sum", "Inscribed Angle Theorem", "Circumscribed Angle Theorem" ] } ## Find the central angle $ \angle COB $ $$ \begin{aligned} &\angle CDB = 48^\circ \ &\angle COB = 2 \times \angle CDB = 2 \times 48^\circ = 96^\circ \end{aligned} $$ ## Apply the tangent properties and quadrilateral angle sum $$ \begin{aligned} &\angle ACO = 90^\circ \ &\angle ABO = 90^\circ \ &\angle A + \angle ACO + \angle ABO + \angle COB = 360^\circ \ &\angle A + 90^\circ + 90^\circ + 96^\circ = 360^\circ \ &\angle A = 180^\circ - 96^\circ = 84^\circ \end{aligned} $$ What is the measure of $\angle A$? 84$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Circumscribed Angle Theorem" ] }

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Question

Explanation:

Find the central angle \( \angle COB \)

Apply the tangent properties and quadrilateral angle sum

Answer: