SAT Question f7dbde16: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice D is correct. Two triangles are similar if they have three pairs of congruent corresponding angles. It's given that angles $L$ and $R$ each measure $60^{\circ }$, and so these corresponding angles are congruent. If angle $M$ is $70^{\circ }$, then angle $N$ must be $50^{\circ }$ so that the sum of the angles in triangle $LMN$ is $180^{\circ }$. If angle $T$ is $50^{\circ }$, then angle $S$ must be $70^{\circ }$ so that the sum of the angles in triangle $RST$ is $180^{\circ }$. Therefore, if the measures of angles $M$ and $T$ are $70^{\circ }$ and $50^{\circ }$, respectively, then corresponding angles $M$ and $S$ are both $70^{\circ }$, and corresponding angles $N$ and $T$ are both $50^{\circ }$. It follows that triangles $LMN$ and $RST$ have three pairs of congruent corresponding angles, and so the triangles are similar. Therefore, the additional piece of information that is sufficient to prove that triangle $LMN$ is similar to triangle $RST$ is that the measures of angles $M$ and $T$ are $70^{\circ }$ and $50^{\circ }$, respectively.