Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-6 Proving Angles Congruent - Practice and Problem-Solving Exercises - Page 127: 39



Work Step by Step

Let $\angle A$ be the angle in question. Let C be the measure of its complement and S be the measure of its supplement. $S=4C\longrightarrow$ given $m\angle A+S=180\longrightarrow$ definition of supplementary $m\angle A=180-S\longrightarrow$ subtraction property of equality $m\angle A+C=90\longrightarrow$ definition of complementary $m\angle A=90-C\longrightarrow$ subtraction property of equality $180-S=90-C\longrightarrow$ transitive property of equality $180-4C=90-C\longrightarrow$ substitution $180=90+3C\longrightarrow$ addition property of equality $90=3C\longrightarrow$ subtraction property of equality $30=C\longrightarrow$ division property of equality Substitute to find the measure of the angle. $m\angle A + C=90\longrightarrow$ definition of complementary $m\angle A+30=90\longrightarrow$ substitution $m\angle A=60\longrightarrow$ subtraction property of equality
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