SAT Question 9d078710: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice B is incorrect. The angle measuring $x^{\circ }$ and the angle measuring $40^{\circ }$ are alternate interior angles. Thus, if lines $j$ and $k$ are parallel, $x$ is equal to $40$, not $140$.

Choice C is incorrect. The angle measuring $y^{\circ }$ and the angle measuring $40^{\circ }$ are vertical angles. Thus, $y=40$, whether lines $j$ and $k$ are parallel or not.

Choice D is incorrect. The angle measuring $z^{\circ }$ is supplementary to the angle measuring $40^{\circ }$. Thus, $z=180-40$, or $z=140$, whether lines $j$ and $k$ are parallel or not.