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 - 3-3 Proving Lines Parallel - Practice and Problem-Solving Exercises: 31

Answer

$x=10$ $m\angle1=70$ $m\angle2=70$

Work Step by Step

Angles 1 and 2 are in corresponding positions relative to the 4 angles created when the transversal intersects with line r and the 4 angles created when the transversal intersects with line s. The Converse of the Corresponding Angles Theorem tells us that the lines are parallel when $\angle1\cong\angle2$, or, by the definition of congruency, when $m\angle1=m\angle2$. Write and solve an equation to find the value of x when the lines are parallel. $m\angle1=m\angle2\longrightarrow$ $80-x=90-2x\longrightarrow$ substitution $80+x=90\longrightarrow$ addition property of equality $x=10\longrightarrow$ subtraction property of equality Substitute to find the measue of each angle. $m\angle1=80-x=80-10=70$ $m\angle2=90-2x=90-2(10)=90-20=70$
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