angle measures and segment lengths
solve for measure of angle a.
$a = ?^\circ$
if 2 secant lines intersect outside a circle: $\angle a = \frac{\widehat{c} - \widehat{b}}{2}$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Angles Outside Circle Theorem", "Secant-Secant Angle" ], "new_concepts": [], "current_concepts": [ "Angles Outside Circle Theorem", "Secant-Secant Angle" ] } ## Identify the given values Using the **Angles Outside Circle Theorem** and **Secant-Secant Angle** knowledge points $$ \begin{aligned} &\text{Far intercepted arc } (c) = 140^\circ\ &\text{Near intercepted arc } (b) = 96^\circ \end{aligned} $$ ## Apply the angle formula Using the **Angles Outside Circle Theorem** and **Secant-Secant Angle** knowledge points $$ \begin{aligned} a &= \frac{c - b}{2}\ a &= \frac{140^\circ - 96^\circ}{2}\ a &= \frac{44^\circ}{2}\ a &= 22^\circ \end{aligned} $$ Solve for measure of angle a. $a =$ $22$$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Secant-Secant Angle" ] }

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Question

Explanation:

Identify the given values

Apply the angle formula

Answer: