Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - Chapter 3 Test: 22

Answer

The measure of angle A is 60 degrees. The measure of angle B is 30 degrees. The measure of angle C is 90 degrees.

Work Step by Step

Let x represent the measure of angle A. The measure of angle C is one-half the measure of angle A. One-half the measure of angle A means $\frac{1}{2}$ $\times$ x = $\frac{x}{2}$. So, the measure of angle C is $\frac{x}{2}$. The measure of angle B is 30 more than the measure of angle A. 30 more than the measure of angle A means 30 + x. So, the measure of angle B is 30 + x. The sum of the angles of every triangle equals 180 degrees. So, we set up the following equation: x + $\frac{x}{2}$ + 30 + x = 180 x + $\frac{x}{2}$ + x = 150 2x + $\frac{x}{2}$ = 150 Multiply both sides by 2: 4x + x = 300 5x = 300 Divide both sides by 5: x = 60 The measure of angle A is 60 degrees. The measure of angle B is $\frac{60}{2}$ = 30 degrees. The measure of angle C is 30 + 60 = 90 degrees.
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