SAT Question 087cdcfd: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. The angle that is shown as lying between the $y^{\circ }$ angle and the $z^{\circ }$ angle is a vertical angle with the $x^{\circ }$ angle. Since vertical angles are congruent and $x=65$, the angle between the $y^{\circ }$ angle and the $z^{\circ }$ angle measures $65^{\circ }$. Since the $65^{\circ }$ angle, the $y^{\circ }$ angle, and the $z^{\circ }$ angle are adjacent and form a straight angle, it follows that the sum of the measures of these three angles is $180^{\circ }$, which is represented by the equation $65^{\circ }+y^{\circ }+z^{\circ }=180^{\circ }$. It's given that $y=75$. Substituting $75$ for $y$ yields $65^{\circ }+75^{\circ }+z^{\circ }=180^{\circ }$, which can be rewritten as $140^{\circ }+z^{\circ }=180^{\circ }$. Subtracting $140^{\circ }$ from both sides of this equation yields $z^{\circ }=40^{\circ }$. Therefore, $z=40$.