unit exam - circles

solve for measure of angle a.

a = ?

if 2 secant lines intersect outside a circle: \angle a = \frac{\widehat{c} - \widehat{b}}{2}

Question

unit exam - circles

solve for measure of angle a.

a = ?

if 2 secant lines intersect outside a circle: \angle a = \frac{\widehat{c} - \widehat{b}}{2}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "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 arc measures $$ \begin{aligned} &\text{Far arc } (c) = 140^\circ\ &\text{Near arc } (b) = 96^\circ \end{aligned} $$ ## Apply the intersecting secants theorem formula $$ \begin{aligned} a &= \frac{c - b}{2}\ a &= \frac{140^\circ - 96^\circ}{2} \end{aligned} $$ ## Calculate the value of angle a $$ \begin{aligned} a &= \frac{44^\circ}{2}\ a &= 22^\circ \end{aligned} $$ Solve for measure of angle a. $a =$ 22$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Outside Circle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given arc measures

Apply the intersecting secants theorem formula

Calculate the value of angle a

Answer: