question 22 of 25

if the measure of a tangent-chord angle is $68^\circ$, then what is the measure of the intercepted arc inside the angle?

a. $68^\circ$
b. $112^\circ$
c. $34^\circ$
d. $136^\circ$

Question

question 22 of 25

if the measure of a tangent-chord angle is $68^\circ$, then what is the measure of the intercepted arc inside the angle?

a. $68^\circ$
b. $112^\circ$
c. $34^\circ$
d. $136^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Theorems" ], "new_concepts": [ "Tangent-Chord Theorem" ], "current_concepts": [ "Circle Theorems", "Tangent-Chord Theorem" ] } ## Identify the relationship between a tangent-chord angle and its intercepted arc $$ \text{Angle} = \frac{1}{2} \times \text{Arc} $$ ## Calculate the measure of the intercepted arc $$ \begin{aligned} 68^\circ &= \frac{1}{2} \times \text{Arc} \ \text{Arc} &= 2 \times 68^\circ \ \text{Arc} &= 136^\circ \end{aligned} $$

A. $68^\circ$

B. $112^\circ$

C. $34^\circ$

D. $136^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Chord Theorem" ] }

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Question

Explanation:

Identify the relationship between a tangent-chord angle and its intercepted arc

Calculate the measure of the intercepted arc

Answer: