Geometry

Question Analysis

The main focus is leveraging the property of an inscribed angle in a semi - circle being a right angle and the inscribed - angle theorem.

 

Key Concept Explanation

1. Inscribed Angle in a Semicircle: An inscribed angle subtended by a diameter (in a semi - circle) is a right angle, measuring .

2. Inscribed Angle Theorem: The measure of an inscribed angle is half of the measure of the arc it intercepts.

 

Step - by - Step Solution

1. Since is the diameter, by the "Inscribed Angle in a Semicircle" property, .

In , given , using the triangle angle - sum property (), we find as follows:

.

2. According to the "Inscribed Angle Theorem", the measure of an inscribed angle () is half of the measure of the arc it intercepts (arc ).

We know the measure of arc

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