Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 6 - Review Exercises: 12

Answer

Angle 1: 50 degrees Angle 2: 40 degrees Angle 3: 90 degrees Angle 4: 50 degrees

Work Step by Step

Angle 3 is 90 degrees, for an inscribed angle is half of the value of the angle of the corresponding arc (the corresponding arc has an angle of 180 degrees). Angle 1, therefore, equals $180-90-40=50$ degrees. Since angle 1 corresponds to arc CB, arc CB is twice the measure of angle 1, making it 100 degrees. Angle 4 is half the measure of arc CB, so it is 50 degrees. Thus, angle 2 is: $180-90-50=40$ degrees.
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