Geometry

Question Analysis

The main focus is using the property that congruent chords in a circle subtend congruent arcs. We'll set up an equation based on the equality of arc measures corresponding to congruent chords to find .

 

Key Concept Explanation

In a circle, if two chords are congruent (shown by the markings), the arcs they subtend have equal measures. This allows us to equate the expressions for the arc measures.

 

Step - by - Step Solution

1. Since chords  and  are congruent, arc  and arc  have equal measures.

Given arc  and arc

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