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 - Review Exercises - Page 316: 30

Answer

Angle 1: 93 degrees Angle 2: 25 degrees Angle 3: 43 degrees Angle 4: 68 degrees Angle 5: 90 degrees Angle 6: 22 degrees Angle 7: 68 degrees Angle 8: 22 degrees Angle 9: 50 degrees Angle 10: 112 degrees

Work Step by Step

An inscribed angle is half of the length of the corresponding arc. Thus: Angle 5 = $.5(180) = 90^{\circ}$ Angle 4 = $.5(136) = 68^{\circ}$ Angle 7 = $.5(136) = 68^{\circ}$ The sum of the measures of angles of a triangle is 180 degrees. Thus: Angle 8 = $180 - 90 - 68 = 22^{\circ}$ The measure of an angle in the center of the circle is equal to the measure of the corresponding arc. Thus: Angle 9 = $50^{\circ}$ We find angle 2: Angle 2 = $180 - .5(50) - 130 = 25^{\circ}$ Thus, we find angle 6: Angle 6 = $180 - 68 - 90 = 22^{\circ}$ Using the fact that angle ADB equals 65 degrees, we obtain: Angle 1 = $ 180 - 22 - 65 = 93^{\circ}$ This makes angle 10: Angle 10 = $ 180 - 43 - 25 = 112^{\circ}$ Finally, we find angle 3: Angle 3 = $ 180 - 112 -25 = 43^{\circ}$
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