SAT Question 686b5212: Lines, Angles, and Triangles answer and explanation with Desmos solution

Based on the figure, the angle with measure $y^{\circ }$ and the angle vertical to the angle with measure $58^{\circ }$ are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure $58^{\circ }$ also has measure $58^{\circ }$. It's given that lines $q$ and $r$ are parallel. Therefore, same side interior angles between lines $q$ and $r$ are supplementary. It follows that $y+58=180$. If $y=2x+8$, then the value of $x$ can be found by substituting $2x+8$ for $y$ in the equation $y+58=180$, which yields $\left(2x+8\right)+58=180$, or $2x+66=180$. Subtracting $66$ from both sides of this equation yields $2x=114$. Dividing both sides of this equation by $2$ yields $x=57$. Thus, if $y=2x+8$, the value of $x$ is $57$.