Geometry: Common Core (15th Edition)

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

Chapter 3 - Parallel and Perpendicular Lines - 3-2 Properties of Parallel Lines - Practice and Problem-Solving Exercises - Page 154: 19


x=135, y=45

Work Step by Step

The angle marked $x$ and the angle marked $3y$ form a corresponding angle pair. The corresponding angle theorem tells us they are congruent. $x=3y\longrightarrow$ definition of congruent The angle marked $x$ and the angle marked $y$ form a linear pair, so they are supplementary. $x+y=180\longrightarrow$ definition of supplementary $3y+y=180\longrightarrow$ substitution $4y=180\longrightarrow$ combine like terms $y=45\longrightarrow$ division property of equality Substitute in the first equation to find the value of x. $x=3y=3(45)=135$
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