SAT Question b434e103: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. The sum of the measures of the angles of a triangle is $180^{\circ }$. Therefore, the sum of the measures of $\angle R$, $\angle S$, and $\angle T$ is $180^{\circ }$. It's given that the measure of $\angle R$ is $63^{\circ }$. It follows that the sum of the measures of $\angle S$ and $\angle T$ is ${\left(180-63\right)}^{\circ }$, or $117^{\circ }$. Therefore, the measure of $\angle S$, in degrees, must be less than $117$. Of the given choices, only $116$ is less than $117$. Thus, the measure, in degrees, of $\angle S$ could be $116$.