Geometry

Question Analysis

The main focus is on using the relationship between inscribed angles and their intercepted arcs. Given the measure of an inscribed angle, we need to find the measure of the arc it intercepts.

 

Key Concept Explanation

An inscribed angle in a circle is an angle whose vertex lies on the circle and whose sides are chords of the circle. The measure of an inscribed angle is always half of the measure of the arc that it intercepts.

 

Step - by - Step Solution

1. We know that the measure of inscribed angle .

2. According to the inscribed - angle property, if  is the inscribed angle and  is the intercepted arc, then .

3. To find , we can re - arrange the formula:

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