Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 287: 36

Answer

When an angle is inscribed in a circle, its value is equal to half of the value of the arc that intersects it. Since the circle is a semicircle, its angle is half of that of a regular circle, meaning that its angle is half of 360 degrees (which is 180 degrees). Since when an angle is inscribed in a circle, its value is equal to half of the value of the arc that intersects it, it follows that the inscribed angle is equal to 90 degrees, which is a right angle.
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