SAT Question 1318dfea: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. It's given that $WZ$ and $XY$ intersect at point $Q$. It follows that $\angle WQX$ and $\angle YQZ$ are vertical angles, which means they are congruent to each other. The figure shows that $\angle W$ and $\angle Y$ both have a measure of $a^{\circ }$, so they are congruent to each other. Therefore, $△QWX$ and $△QYZ$ are similar triangles, where $WQ$ corresponds to $YQ$ and $WX$ corresponds to $YZ$. Since the lengths of corresponding sides in similar triangles are proportional, it follows that $\frac{YZ}{YQ}=\frac{WX}{WQ}$. It's given that $YQ=21$, $WQ=70$, and $WX=60$. Substituting $21$ for $YQ$, $70$ for $WQ$, and $60$ for $WX$ in the equation $\frac{YZ}{YQ}=\frac{WX}{WQ}$ yields $\frac{YZ}{21}=\frac{60}{70}$, or $\frac{YZ}{21}=\frac{6}{7}$. Multiplying each side of this equation by $21$ yields $YZ=18$. Therefore, the length of $YZ$ is $18$.