SAT Question ffc39dc5: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. It’s given that $CD=EF$ and $FC=DE$, and the figure shows that $\overline{DF}$ is a side of both $△CDF$ and $△EFD$. Since $△CDF$ and $△EFD$ have three pairs of congruent sides, the triangles are congruent, where $\angle CFD$ corresponds to $\angle EDF$ and $\angle CDF$ corresponds to $\angle EFD$. It’s given that the measure of $\angle EDF$ is $65^{\circ }$ and the measure of $\angle EFD$ is $30^{\circ }$. Since corresponding angles of congruent triangles are congruent, $\angle CFD$ is congruent to $\angle EDF$ and $\angle CDF$ is congruent to $\angle EFD$. Therefore, the measure of $\angle CFD$ is $65^{\circ }$ and the measure of $\angle CDF$ is $30^{\circ }$. Since $\angle CDE$ is made up of $\angle CDF$ and $\angle EDF$, it follows that the measure of $\angle CDE$ is equal to the sum of the measures of $\angle CDF$ and $\angle EDF$. Therefore, the measure of $\angle CDE$ is equal to $(30+65{)}^{\circ }$, or $95^{\circ }$.