Geometry

Question Analysis

The main focus is on using the property that an inscribed angle in a semicircle is a right angle and then applying the angle - sum property of a triangle to 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, which measures . 

So, in , . Also, since  (radii of the same circle), .

2. Angle - sum property of a triangle: The sum of the interior angles of a triangle is , i.e., for , .

Step-by-Step Solution  

1. Set up the equation using the angle - sum property:

Since and

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