question 20 of 25

a tangent-tangent angle intercepts two arcs that measure $124^\circ$ and $236^\circ$.
what is the measure of the tangent-tangent angle?

a. $56^\circ$
b. $112^\circ$
c. $180^\circ$
d. $224^\circ$

Question

question 20 of 25

a tangent-tangent angle intercepts two arcs that measure $124^\circ$ and $236^\circ$.
what is the measure of the tangent-tangent angle?

a. $56^\circ$
b. $112^\circ$
c. $180^\circ$
d. $224^\circ$

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-Tangent Angle Theorem" ], "current_concepts": [ "Circle Theorems", "Tangent-Tangent Angle Theorem" ] } ## Identify the given arc measures $$ \begin{aligned} &\text{Major Arc} = 236^\circ\ &\text{Minor Arc} = 124^\circ \end{aligned} $$ ## Apply the Tangent-Tangent Angle Theorem $$ \begin{aligned} \text{Angle} &= \frac{\text{Major Arc} - \text{Minor Arc}}{2}\ \text{Angle} &= \frac{236^\circ - 124^\circ}{2} \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} \text{Angle} &= \frac{112^\circ}{2} = 56^\circ \end{aligned} $$

A. $56^\circ$

B. $112^\circ$

C. $180^\circ$

D. $224^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given arc measures

Apply the Tangent-Tangent Angle Theorem

Calculate the final angle measure

Answer: