solve for measure of angle a.

(a = ?^{\circ})

if two chords intersect inside a circle: $\angle a = \frac{\widehat{b} + \widehat{c}}{2}$

Question

solve for measure of angle a.

(a = ?^{\circ})

if two chords intersect inside a circle: $\angle a = \frac{\widehat{b} + \widehat{c}}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Angles Inside Circle Theorem", "Intersecting Chords Angle" ], "new_concepts": [], "current_concepts": [ "Angles Inside Circle Theorem", "Intersecting Chords Angle" ] } ## Identify the given arc measures and formula $$ \begin{aligned} &\text{Arc } 1 = 41^\circ\ &\text{Arc } 2 = 29^\circ\ &\angle a = \frac{\text{Arc } 1 + \text{Arc } 2}{2} \end{aligned} $$ ## Calculate the measure of angle a $$ \begin{aligned} &a = \frac{41 + 29}{2}\ &a = \frac{70}{2}\ &a = 35 \end{aligned} $$ Solve for measure of angle a. $a =$ 35$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Inside Circle Theorem" ] }

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Explanation:

Identify the given arc measures and formula

Calculate the measure of angle a

Answer: