Geometry

Question Analysis

The main focus is on using the properties of angles in a semi - circle and the relationship between inscribed angles and intercepted arcs.

 

Key Concept Explanation

1. Inscribed Angle in a Semicircle: An inscribed angle subtended by a diameter is a right angle ().

2. Triangle Angle - Sum Property: The sum of the interior angles of a triangle is .

3. Relationship between Inscribed Angle and Intercepted Arc: 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, .

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

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