Question

1. determine the value of x for which r || s if

• m∠1 = 80 - x, and
• m∠2 = 90 - 2x.

Explanation:

Step1: Use corresponding - angles property

When $r\parallel s$, $\angle1$ and $\angle2$ are corresponding angles, so $m\angle1 = m\angle2$.
$80 - x=90 - 2x$

Step2: Solve the equation for $x$

Add $2x$ to both sides:
$80 - x+2x=90 - 2x+2x$
$80 + x=90$
Subtract 80 from both sides:
$x=90 - 80$
$x = 10$

Answer:

10