Geometry

Question Analysis

This question focuses on applying the Intersecting Chords Angle Theorem. First, we need to find the supplementary angle of the given angle formed by the intersecting chords. Then, using the known measure of one intercepted arc, we can determine 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 to 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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