SAT Question ecc98c87: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is incorrect. The angle labeled $x^{\circ }$ forms a linear pair with the angle labeled $w^{\circ }$, so $x=180-147$, or $x=33$, regardless of whether lines $r$ and $s$ are parallel.

Choice C is incorrect. Substituting $147$ for $w$ in this equation yields $147+y=180$, or $y=33$. Since the angle labeled $w^{\circ }$ and the angle labeled $y^{\circ }$ are corresponding angles, if $w$ and $y$ aren’t equal, then lines $r$ and $s$ can’t be parallel.

Choice D is incorrect. The relationship $y+z=180$ describes a linear pair at line $s$, which is true regardless of whether lines $r$ and $s$ are parallel.