Geometry

Question Analysis

This question focuses on applying the Outside Angle Theorem. We are given the measure of the major arc intercepted by two tangents  and  from an external point  to the circle. The goal is to find the measure of  using the relationship between the angle and the intercepted arcs.

 

Step - by - Step Solution

1. Find the measure of the minor arc:

The measure of the major arc . Since the sum of the major and minor arcs is , the measure of the minor arc .

2. Apply the Outside Angle Theorem:

Substitute