Answer
$x=5$
$m\angle1=50$
$m\angle2=50$
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.
$m\angle1=60-2x=60-2(5)=60-10=50$
$m\angle2=70-4x=70-4(5)=70-20=50$
