Answer
$I$
Work Step by Step
A transversal intersects the parallel lines $g$ and $h$. Therefore, same-side interior angles are supplementary.
The angles whose measures are given by expressions in the diagram are same-side interior angles; therefore, we can add these expressions together and set them equal to $180^{\circ}$ to find the value of $x$:
$(2x + 10) + (5x - 5) = 180$
Group like terms together on the left side of the equation:
$(2x + 5x) + (10 - 5) = 180$
Combine like terms to simplify:
$(7x) + (5) = 180$
Subtract $5$ from each side of the equation to move constants to the right side of the equation:
$7x = 175$
Divide each side of the equation by $7$ to solve for $x$:
$x = 25$
This corresponds to answer option $I$.
