Question

1. find x

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, we set up the equation based on the equality of vertical angles. For the first pair of vertical angles: $x + 12=4y - 18$ (but we focus on the second figure). In the second figure, since vertical angles are equal, we have the equation $x + 23=2x+31$.

Step2: Solve the equation for x

Subtract x from both sides of the equation $x + 23=2x+31$.
$x+23 - x=2x + 31 - x$
$23=x + 31$.
Then subtract 31 from both sides:
$23-31=x+31 - 31$
$- 8=x$.

Answer:

$x=-8$