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.
$m\angle1=80-x=80-10=70$
$m\angle2=90-2x=90-2(10)=90-20=70$
