Geometry

Question Analysis

The main focus is on using the property of inscribed angles and the sum of arcs in a circle. We know the measure of one arc and one inscribed angle, and we need to find another inscribed angle. First, we'll find the measure of the relevant arc, then use the inscribed - angle property.

 

Key Concept Explanation

1. The measure of an inscribed angle is half of the measure of the arc it intercepts.

2. The sum of the measures of the arcs of a circle is .

 

Step - by - Step Solution

1. First, find the measure of arc .

The sum of the arcs in a circle is . Given arc .

Let arc . Then .

We know that the inscribed angle , and by the inscribed - angle property, the arc that it intercepts has a measure of .

So, , which gives

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