SAT Question 5207e508: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice D is correct. It's given that lines $m$ and $n$ are parallel. Since line $t$ intersects both lines $m$ and $n$, it's a transversal. The angles in the figure marked as $170^{\circ }$ and $w^{\circ }$ are on the same side of the transversal, where one is an interior angle with line $m$ as a side, and the other is an exterior angle with line $n$ as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that $w^{\circ }=170^{\circ }$. Therefore, the value of $w$ is $170$.