Geometry

Question Analysis

The main focus is on using the property that an inscribed angle in a semi - circle is 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, which is .

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 can 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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