Question

line r intersects lines p and q. for what value of x are lines p and q parallel? x = □

Explanation:

Step1: Identify corresponding angles

When lines $p$ and $q$ are parallel, the angle measuring $102^{\circ}$ and the angle measuring $(5x + 18)^{\circ}$ are corresponding angles and are equal. So we set up the equation $5x+18 = 102$.

Step2: Solve the equation for $x$

Subtract 18 from both sides of the equation: $5x=102 - 18$. So $5x=84$. Then divide both sides by 5: $x=\frac{84}{5}=16.8$.

Answer:

$16.8$