## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 2 - Reasoning and Proof - 2-6 Proving Angles Congruent - Practice and Problem-Solving Exercises - Page 127: 35

#### Answer

x=50 y=20 The angles measure 80, 100 and 80.

#### Work Step by Step

Use the definition of a linear pair and substitution to write and solve equations. Solve for x. $4y+2x=180\longrightarrow$ a linear pair is supplementary $2x=180-4y\longrightarrow$ subtraction property of equality $x=90-2y\longrightarrow$ division property of equality Solve for y. $2x+(x+y+10)=180\longrightarrow$ a linear pair is supplementary $3x+y+10=180\longrightarrow$ combine like terms $3(90-2y)+y+10=180\longrightarrow$ substitute for x $270-6y+y+10=180\longrightarrow$ distributive property $280-5y=180\longrightarrow$ combine like terms $-5y=-100\longrightarrow$ subtration property of equality $y=20\longrightarrow$ division property of equality Substitute to find x. $x=90-2y=90-2(20)=90-40=50$ Substitute to find the measure of each angle. $4y=4(20)=80$ $2x=2(50)=100$ $x+y+10=50+20+10=80$

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