SAT Question 5733ce30: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice D is correct. Since $\angle BCD$ and $\angle BCA$ form a linear pair of angles, their measures sum to $180^{\circ }$. It's given that the measure of $\angle BCD$ is $110^{\circ }$. Therefore, $110^{\circ }+\angle BCA=180^{\circ }$. Subtracting $110^{\circ }$ from both sides of this equation gives the measure of $\angle BCA$ as $70^{\circ }$. It's also given that the measure of $\angle BAC$ is equal to the measure of $\angle BCA$. Thus, the measure of $\angle BAC$ is also $70^{\circ }$. The measures of the interior angles of a triangle sum to $180^{\circ }$. Thus, $70^{\circ }+70^{\circ }+x^{\circ }=180^{\circ }$. Combining like terms on the left-hand side of this equation yields $140^{\circ }+x^{\circ }=180^{\circ }$. Subtracting $140^{\circ }$ from both sides of this equation yields $x^{\circ }=40^{\circ }$, or $x=40$.