Geometry

Question Analysis

The main focus is on the property that congruent chords in a circle subtend congruent arcs. We'll use this property to set up an equation with the given arc - measure expressions and solve for .

 

Key Concept Explanation

In a circle, when two chords are congruent (as indicated by the equal markings in the diagram), 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, the measures of arc  and arc  are equal.

We are given that the measure of arc  is  and the measure of arc  is

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