Answer
$x=1.25$
$m\angle1=10$
$m\angle2=10$
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.
$m\angle1=m\angle2$
$20-8x=30-16x\longrightarrow$ substitution
$20+8x=30\longrightarrow$ addition property of equality
$8x=10\longrightarrow$ subtraction property of equality
$x=1.25\longrightarrow$ division property of equality
Substitute to find the measue of each angle.
$m\angle1=20-8x=20-8(1.25)=20-10=10$
$m\angle2=30-16x=30-16(1.25)=30-20=10$
