Answer
$x=2.5$
$m\angle1=30$
$m\angle2=30$
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.
$m\angle1=m\angle2$
$40-4x=50-8x\longrightarrow$ substitution
$40+4x=50\longrightarrow$ addition property of equality
$4x=10\longrightarrow$ subtraction property of equality
$x=2.5\longrightarrow$ division property of equality
Substitute to find the measue of each angle.
$m\angle1=40-4x=40-4(2.5)=40-10=30$
$m\angle2=50-8x=50-8(2.5)=50-20=30$
