Geometry

Question Analysis

This question requires applying the Intersecting Chords Angle Theorem. We are given the measure of the angle formed by two intersecting chords and the measure of one intercepted arc . The objective is to find the measure of the other intercepted arc .

 

Key Concept Explanation

Intersecting Chords Angle Theorem: When two chords intersect inside a circle, the measure of the angle formed is equal to half the sum of the measures of the arcs intercepted by the angle. Mathematically, if the angle is and the intercepted arcs are and , then .

 

Step - by - Step Solution

1. Apply the Intersecting Chords Angle Theorem:

According to the theorem, .

2. Substitute the known values:

We know that and . S...