Geometry

Question Analysis

The main focus is applying the Intersecting Chords Angle Theorem. We first find the angle  which is supplementary to . Then, using the known measure of one intercepted arc  and the Intersecting Chords Angle Theorem, we can find the measure of the other intercepted arc .

 

Key Concept Explanation

Intersecting Chords Angle Theorem: The measure of the angle formed by two intersecting chords in a circle is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle. That is, if two chords intersect and form an angle , and the intercepted arcs are  and , then .

 

Step - by - Step Solution

1. First, find :

Since , and  and  are supplementary, so .

2. Apply the Intersecting Chords Angle Theorem:

According to the theorem,

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