SAT Question 8364487a: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. It’s given that triangle $TUV$ is dilated by a scale factor of $\frac{1}{2}$ to obtain triangle $T^{{}^{\prime }}{U}^{{}^{\prime }}{V}^{{}^{\prime }}$, where $T$ corresponds to $T^{{}^{\prime }}$ and $U$ corresponds to $U^{{}^{\prime }}$. A dilation is a transformation that multiplies all side lengths by the same scale factor while preserving angle measures. Therefore, corresponding angles in triangles $TUV$ and $T^{{}^{\prime }}{U}^{{}^{\prime }}{V}^{{}^{\prime }}$ are equal. Since $V$ corresponds to $V^{{}^{\prime }}$, the measure of angle $V^{{}^{\prime }}$ is equal to the measure of angle $V$. The figure shows that the measure of angle $V$ is $25^{\circ }$, so it follows that the measure of angle $V^{{}^{\prime }}$ is also $25^{\circ }$.