bcd is a circumscribed angle of circle a. angle measures $53^\circ$

what is the measure of angle bcd?

$37^\circ$
$53^\circ$
$74^\circ$
$106^\circ$

Question

bcd is a circumscribed angle of circle a. angle measures $53^\circ$

what is the measure of angle bcd?

$37^\circ$
$53^\circ$
$74^\circ$
$106^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circumscribed Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Circumscribed Angle Theorem", "Circle Geometry" ] } ## Identify the relationship between the circumscribed angle and the central angle $$ \angle BCD + \angle BAD = 180^\circ $$ ## Substitute the given central angle measure $$ \begin{aligned} \angle BAD &= 106^\circ \quad (\text{since } \angle BAC = 53^\circ \text{ and } \angle BAD = 2 \times 53^\circ) \ \angle BCD + 106^\circ &= 180^\circ \end{aligned} $$ ## Solve for the measure of angle BCD $$ \angle BCD = 180^\circ - 106^\circ = 74^\circ $$

37°

53°

74°

106°

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

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between the circumscribed angle and the central angle

Substitute the given central angle measure

Solve for the measure of angle BCD

Answer:

Identify the relationship between the circumscribed angle and the central angle

Substitute the given central angle measure

Solve for the measure of angle BCD