Answer
$G$
Work Step by Step
The trapezoid depicted has one set of parallel lines. We can visualize the right side of the trapezoid as being like a transversal that is running through the parallel lines. If this is the case, then the two angles labeled are same-side interior angles.
According to the same-side interior angle theorem, if two parallel lines are cut by a transversal, then same-side interior angles are supplementary, meaning their measurements add up to $180^{\circ}$. With this theorem in mind, let us set up the equation to reflect this:
$130 + 2x = 180$
Subtract $130$ from each side of the equation to isolate the $x$ term:
$130 - 130 + 2x = 180 - 130$
Subtract to simplify:
$2x = 50$
Divide both sides by $2$ to solve for $x$:
$x = 25$
This corresponds to option $G$.
