Question

lines p and q are intersected by transversal t as shown. what value of x proves that lines p and q are parallel? (3x + 18)° (6x - 18)°

Explanation:

Step1: Identify angle - relationship

When lines $p$ and $q$ are parallel, the corresponding angles are equal. So, $3x + 18=6x - 18$.

Step2: Rearrange the equation

Subtract $3x$ from both sides: $18 = 6x-3x - 18$, which simplifies to $18 = 3x-18$.

Step3: Solve for $x$

Add 18 to both sides: $18 + 18=3x$, so $36 = 3x$. Then divide both sides by 3: $x=\frac{36}{3}=12$.

Answer:

$12$