Question

1. lines p and q are intersected by line r, as shown below. if m∠1 = 7x - 36 and m∠2 = 5x + 12, for which value of x would p || q?

Explanation:

Step1: Identify angle - relationship

When $p\parallel q$, $\angle1$ and $\angle2$ are corresponding angles, so $m\angle1 = m\angle2$.

Step2: Set up the equation

Set $7x - 36=5x + 12$.

Step3: Solve for $x$

Subtract $5x$ from both sides: $7x-5x - 36=5x-5x + 12$, which simplifies to $2x-36 = 12$.
Then add 36 to both sides: $2x-36 + 36=12 + 36$, getting $2x=48$.
Divide both sides by 2: $\frac{2x}{2}=\frac{48}{2}$, so $x = 24$.

Answer:

$x = 24$