Lines, angles, and triangles SAT question

Choice B is correct. In the figure shown, the angle measuring $y^{\circ }$ is congruent to its vertical angle formed by lines $s$ and $m$, so the measure of the vertical angle is also $y^{\circ }$. The vertical angle forms a same-side interior angle pair with the angle measuring $x^{\circ }$. It's given that lines $r$ and $s$ are parallel. Therefore, same-side interior angles in the figure are supplementary, which means the sum of the measure of the vertical angle and the measure of the angle measuring $x^{\circ }$ is $180^{\circ }$, or $x+y=180$. Subtracting $x$ from both sides of this equation yields $y=180-x$. Substituting $180-x$ for $y$ in the inequality $y<65$ yields $180-x<65$. Adding $x$ to both sides of this inequality yields $180<65+x$. Subtracting $65$ from both sides of this inequality yields $115<x$, or $x>115$. Thus, if $y<65$, it must be true that $x>115$.

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

Choice C is incorrect. $x+y$ must be equal to, not less than, $180$.

Choice D is incorrect. $x+y$ must be equal to, not greater than, $180$.