Question

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

• m∠1 = 20 - 8x, and
• m∠2 = 30 - 16x.

Explanation:

Step1: Set angles equal

Since $r\parallel s$, $\angle1$ and $\angle2$ are corresponding angles and are equal. So we set up the equation $20 - 8x=30 - 16x$.

Step2: Add $16x$ to both sides

$20 - 8x+16x=30 - 16x+16x$, which simplifies to $20 + 8x=30$.

Step3: Subtract 20 from both sides

$20 + 8x-20=30 - 20$, resulting in $8x = 10$.

Step4: Solve for $x$

Divide both sides by 8: $x=\frac{10}{8}=1.25$.

Answer:

$1.25$