Geometry

Question Analysis

The main focus is on using the property that angles in the same segment of a circle and the fact that has as a diameter (so ). We'll set up an equation based on the angle - sum property of a triangle and solve for .

 

Key Concept Explanation

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

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

 

Step - by - Step Solution

1. Since is the diameter, in .

We know and .

2. Using the triangle angle - sum theorem (

Click "Show Answer" to reveal the answer and analysis