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 125: 17


x=14 y=15 The vertical angles measure 50. The other angle measures 130.

Work Step by Step

Use the Vertical Angles Theorem, which tells us that verticals angles have equal measures, to write an equation and solve for x. $3x+8=5x-20$ $3x+28=5x\longrightarrow$ addition property of equality $28=2x\longrightarrow$ subtraction property of equality $14=x\longrightarrow$ division property of equality By definition, linear angles are supplementary. Write an equation and substitute for x to find y. $(3x+8)+(5x+4y)=180$ $8x+8+4y=180\longrightarrow$ combine like terms $8(14)+8+4y=180\longrightarrow$ substitute for x $112+8+4y=180\longrightarrow$ simplify $120+4y=180\longrightarrow$ simplify $4y=60\longrightarrow$ subtraction property of equality $y=15$ Substiute to find the measure of each angle. (The vertical angles have the same measure, so it is only necessary to solve one term.) $3x+8=3(14)+8=42+8=50$ $5x-20=5(14)-20=70-20=50$ $5x+4y=5(14)+4(15)=70+60=130$
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