Geometry

Question Analysis

This question focuses on applying the property that an inscribed angle in a semicircle is a right angle and the triangle angle - sum theorem. Given  and knowing  is the diameter (implying ), we need to find .

 

Key Concept Explanation

1. Inscribed Angle in a Semicircle: An inscribed angle subtended by a diameter (i.e., in a semicircle) is a right angle, measuring .

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

 

Step - by - Step Solution

1. Since  is the diameter of the circle, by the property of an inscribed angle in a semicircle, .

2. In , we know  and .

Using the triangle angle - sum theorem (

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