Geometry

Question Analysis

The main focus is on using the relationship between central angles and inscribed angles that intercept the same arc. We are given expressions for an inscribed angle and a central angle that intercept the same arc . We need to find the value of by applying the property relating these two types of angles.

 

Key Concept Explanation

A central angle has its vertex at the center of the circle, and an inscribed angle has its vertex on the circle. The measure of an inscribed angle that intercepts the same arc as a central angle is half of the measure of the central angle.

 

Step - by - Step Solution

1. We know that the measure of the inscribed angle and the measure of the central angle , and they intercept the same arc .

2. According to the property, . So we set up the equation:

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