SAT Question 2085e10e: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice D is correct. When two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. It's given that in triangle $DEF$, the measure of angle $D$ is $47^{\circ }$ and the measure of angle $E$ is $97^{\circ }$. It's also given that in triangle $RST$, the measure of angle $R$ is $47^{\circ }$ and the measure of angle $S$ is $97^{\circ }$. It follows that angle $D$ is congruent to angle $R$ and that angle $E$ is congruent to angle $S$. Therefore, triangle $DEF$ is similar to triangle $RST$ and no additional information is needed.