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: 34


x=35 y=70 The angles measure 70, 110 and 70.

Work Step by Step

The Vertical Angle Theorem tells us that $y=2x$. Use the definition of a linear pair and substitution to write and solve equations. Solve for x. $y+(x+y+5)=180\longrightarrow$ a linear pair is supplementary $2x+x+2x+5=180\longrightarrow$ substitute $5x+5=180\longrightarrow$ combine like terms $5x=175\longrightarrow$ subtraction property of equality $x=35\longrightarrow$ division property of equality Solve for y. $y=2x=2(35)=70$ Substitute to find the measure of each angle. $y=70$ $x+y+5=35+70+5=110$ $2x=2(35)=70$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.