Geometry

Question Analysis

This question is about using the Intersecting Chords Angle Theorem. The key is to first find the adjacent - supplementary angle of the given angle formed by the intersecting chords, and then use the known measure of one intercepted arc to 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 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 adjacent - 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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