Final Answer:
An inscribed angle intercepts a semicircle, then the angle is a right angle (Theorem 7.5C).
Step-by-step explanation:
Inscribed angles are formed by two chords that intersect on the circumference of a circle. The key insight behind Theorem 7.5C lies in recognizing that when an inscribed angle intercepts a semicircle, it essentially spans half of the circle. A semicircle subtends a 180-degree central angle, and any inscribed angle that intercepts the same arc will be half of this central angle, resulting in a 90-degree angle – a right angle.
To grasp this concept further, consider the properties of circles. A circle comprises 360 degrees, and a semicircle covers half of that, which is 180 degrees. As a result, any angle subtended by the arc of a semicircle must be half of the central angle, making it a right angle. This relationship between inscribed angles and semicircles is a fundamental geometric principle, providing a straightforward method to identify right angles within the context of circles and their inscribed angles.