Chapter 3 - Parallel and Perpendicular Lines - 3-3 Proving Lines Parallel - Practice and Problem-Solving Exercises - Page 162: 32

$x=5$ $m\angle1=50$ $m\angle2=50$

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. $m\angle1=m\angle2$ $60-2x=70-4x\longrightarrow$ substitution $60+2x=70\longrightarrow$ addition property of equality $2x=10\longrightarrow$ subtraction property of equality $x=5\longrightarrow$ division property of equality Substitute to find the measue of each angle. $m\angle1=60-2x=60-2(5)=60-10=50$ $m\angle2=70-4x=70-4(5)=70-20=50$

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