Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - 3.3 - More on Solving Equations and Problem Solving - Problem Set 3.3: 53

Answer

The angles are 32° and 58°.

Work Step by Step

Let X represent one of the angles. The other one is 6° smaller than twice the other angle. Twice the other angle means 2 $\times$ X = 2X. 6° smaller than twice the other angle means 2X - 6. Since the sum of two complementary angles is 90°, one of the angles is X and the other 2X - 6. This lets us set up the following equation: X + 2X - 6 = 90 3X - 6 = 90 Add 6 to both sides 3X = 96 Divide both sides by 3 X = 32 Since X = 32, the first angle is 32°, while the second angle is 2 $\times$ 32 - 6 = 58°
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