Lines, angles, and triangles SAT question

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 $134^{\circ }$ 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 $w^{\circ }=134^{\circ }$. Therefore, the value of $w$ is $134$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.