question 9 of 10

the measure of $\widehat{ab}$ is $126^{\circ}$. what is the measure of $\angle abc$, the tangent-chord angle?

a. $66^{\circ}$
b. $63^{\circ}$
c. $126^{\circ}$
d. $152^{\circ}$

Question

question 9 of 10

the measure of $\widehat{ab}$ is $126^{\circ}$. what is the measure of $\angle abc$, the tangent-chord angle?

a. $66^{\circ}$
b. $63^{\circ}$
c. $126^{\circ}$
d. $152^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Secant-Tangent Angle Theorem", "Arc Measure" ], "new_concepts": [], "current_concepts": [ "Secant-Tangent Angle Theorem", "Arc Measure", "Chord of a Circle", "Tangent Line" ] } ## Identify the given geometric elements Using the *Arc Measure* knowledge point $$ m\widehat{AB} = 126^\circ $$ ## Apply the tangent-chord relationship Using the *Secant-Tangent Angle Theorem* knowledge point $$ m\angle ABC = \frac{1}{2} \cdot m\widehat{AB} $$ ## Calculate the angle measure Using the *Secant-Tangent Angle Theorem* knowledge point $$ m\angle ABC = \frac{1}{2} \cdot 126^\circ = 63^\circ $$

(A) $66^\circ$

(B) $63^\circ$

(C) $126^\circ$

(D) $152^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric elements

Apply the tangent-chord relationship

Calculate the angle measure

Answer: