what is the measure of angle cab in circle o?

$24^\circ$
$48^\circ$
$72^\circ$
$96^\circ$

Question

what is the measure of angle cab in circle o?

$24^\circ$
$48^\circ$
$72^\circ$
$96^\circ$

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 given values and geometric relationships $$ \begin{aligned} &\text{Central angle } \angle COB = 48^\circ \ &\text{Inscribed angle } \angle CAB \text{ intercepts the same arc } \widehat{CB} \end{aligned} $$ ## Apply the Inscribed Angle Theorem $$ \begin{aligned} &m\angle CAB = \frac{1}{2} \cdot m\angle COB \ &m\angle CAB = \frac{1}{2} \cdot 48^\circ = 24^\circ \end{aligned} $$

(A) $24^\circ$

(B) $48^\circ$

(C) $72^\circ$

(D) $96^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values and geometric relationships

Apply the Inscribed Angle Theorem

Answer: