what is the measure of angle coa?
$140^\circ$
$150^\circ$
$160^\circ$
$170^\circ$

Question

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", "Central Angle Theorem" ] } ## Identify the relationship between the inscribed angle and the central angle $$ \begin{aligned} &\angle CBA \text{ is an inscribed angle subtending arc } CA.\ &\angle COA \text{ is the central angle subtending the same arc } CA.\ &\text{Given: } m\angle CBA = 80^\circ \end{aligned} $$ ## Apply the Inscribed Angle Theorem $$ \begin{aligned} &m\angle COA = 2 \cdot m\angle CBA\ &m\angle COA = 2 \cdot 80^\circ\ &m\angle COA = 160^\circ \end{aligned} $$

140°

150°

160°

170°

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

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between the inscribed angle and the central angle

Apply the Inscribed Angle Theorem

Answer: