Question

find the value of x for which r || s. then find m∠1 and m∠2.
m∠1 = 81 - x
m∠2 = 92 - 2x
the value of x for which r || s is
2
m∠1 = 11

Explanation:

Step1: Use the property of parallel lines

When $r\parallel s$, $\angle1$ and $\angle2$ are corresponding angles and are equal. So set up the equation $61 - x=92 - 2x$.

Step2: Solve the equation for $x$

Add $2x$ to both sides: $61 - x+2x=92 - 2x+2x$, which simplifies to $61 + x=92$. Then subtract 61 from both sides: $x=92 - 61$. So $x = 31$.

Step3: Find $m\angle1$

Substitute $x = 31$ into the expression for $m\angle1$. $m\angle1=61 - x=61 - 31=30$.

Step4: Find $m\angle2$

Since $\angle1=\angle2$ when $r\parallel s$, $m\angle2 = 30$.

Answer:

$x = 31$, $m\angle1=30$, $m\angle2 = 30$