SAT Question 345cc36a: Lines, Angles, and Triangles answer and explanation with Desmos solution

The figure shown includes two triangles, triangle $WQX$ and triangle $YQZ$, such that angle $WQX$ and angle $YQZ$ are vertical angles. It follows that angle $WQX$ is congruent to angle $YQZ$. It's also given in the figure that the measures of angle $W$ and angle $Y$ are $a^{\circ }$. Therefore angle $W$ is congruent to angle $Y$. Since triangle $WQX$ and triangle $YQZ$ have two pairs of congruent angles, triangle $WQX$ is similar to triangle $YQZ$ by the angle-angle similarity postulate, where $\overline{YZ}$ corresponds to $\overline{WX}$, and $\overline{YQ}$ corresponds to $\overline{WQ}$. Since the lengths of corresponding sides in similar triangles are proportional, it follows that $\frac{YZ}{WX}=\frac{YQ}{WQ}$. It's given that $YQ=63$, $WQ=70$, and $WX=60$. Substituting $63$ for $YQ$, $70$ for $WQ$, and $60$ for $WX$ in the equation $\frac{YZ}{WX}=\frac{YQ}{WQ}$ yields $\frac{YZ}{60}=\frac{63}{70}$. Multiplying each side of this equation by $60$ yields $YZ=\left(\frac{63}{70}\right)\left(60\right)$, or $YZ=54$. Therefore, the length of $\overline{YZ}$ is $54$.