SAT Question dfc420b2: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. It's given that $x=100$, so the measure of $\angle ABC$ is $100^{\circ }$. The sum of the measures of the interior angles of any triangle equals $180^{\circ }$. In triangle $ABC$, subtracting the two known angle measures from $180^{\circ }$ gives the third angle measure: $180^{\circ }-100^{\circ }-20^{\circ }=60^{\circ }$. This is the measure of $\angle BCA$. Since $\angle BCA$ and $\angle DCE$ are vertical angles, they are congruent, so the measure of $\angle DCE$ is also $60^{\circ }$. In triangle $CDE$, subtracting the two known angle measures from $180^{\circ }$ gives the third angle measure: $180^{\circ }-60^{\circ }-40^{\circ }=80^{\circ }$. This is the measure of $\angle CDE$. Since the measure of $\angle CDE$ is $y^{\circ }$, the value of $y$ is $80$.