Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapters 1-9 Cumulative Review Problem Set: 87

Answer

65 degrees, 115 degrees

Work Step by Step

Since the two angles are supplementary, their sum is $180$ degrees. Let the smaller angle be $x$. Since the larger angle is $15$ degrees less than twice the smaller angle, the expression for the larger angle is $(2x-15)$. Since the sum of the two angles is 180, we obtain: $x+(2x-15)=180$ $x+2x-15=180$ $3x-15=180$ $3x=180+15$ $3x=195$ $x=\frac{195}{3}=65$ Therefore, the smaller angle is $65$ degrees while the larger angle is $(2x-15)=2(65)-15=130-15=115$ degrees.
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