Geometry

Question Analysis

This question focuses on the application of the Intersecting Chords Angle Theorem. We first need to determine the appropriate angle by finding the supplementary angle of the given intersecting - chords angle. Then, using the known measure of one intercepted arc, 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. That is, if two chords intersect and form an angle , and the intercepted arcs are  and , then .

 

Step - by - Step Solution

1. Find the measure of :

Given that , since  and  are supplementary angles, we have .

2. Apply the Intersecting Chords Angle Theorem:

According to the theorem, for , we get .

We know that

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