Geometry

Question Analysis

This question focuses on applying the Outside Angle Theorem. We are given the measures of two intercepted arcs formed by a tangent  and a secant 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.

 

Key Concept Explanation

Outside Angle Theorem: The measure of an angle formed by two secants, two tangents, or a secant and a tangent from an external point to a circle is equal to half the difference of the measures of the intercepted arcs. If the angle is , the major arc is , and the minor arc is , then .

 

Step - by - Step Solution

1. First, find the measure of the minor arc :

The sum of the measures of arcs in a circle is . Given one arc as  and another as , the measure of the minor arc .

2. Apply the Outside Angle Theorem: