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: 33

Answer

x=30 y=90 angles measure 60, 120 and 60

Work Step by Step

Use the definition of a linear pair to write and solve equations. Solve for y: $(y+x)+(y-x)=180\longrightarrow$ a linear pair is supplementary $2y=180\longrightarrow$ combine like terms $y=90\longrightarrow$ division property of equality Substitute and solve for x: $2x+(y+x)=180\longrightarrow$ a linear pair is supplementary $3x+y=180\longrightarrow$ combine like terms $3x+90=180\longrightarrow$ substitute $3x=90\longrightarrow$ subtraction property of equality $x=30\longrightarrow$ division property of equality Substitute to find the measure of each angle. $2x=2(30)=60$ $y+x=90+30=120$ $y-x=90-30=60$
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