SAT Question 2f7c92ad: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. It's given that triangle $CAE$ is similar to triangle $CBD$. Corresponding angles in similar triangles have equal measure. Angle $BCD$ and angle $ACE$ represent the same angle. It follows that angle $BCD$ and angle $ACE$ have equal measure and are corresponding angles. It's given in the figure that angle $BDC$ and angle $AEC$ are right angles and therefore have equal measure. It follows that angle $BDC$ and angle $AEC$ are corresponding angles. Therefore, angle $CBD$ and angle $CAE$ are corresponding angles and have equal measure. It's given that the measure of angle $CBD$ is $57^{\circ }$, so the measure of angle $CAE$ is $57^{\circ }$.