SAT Question 010243e6: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. Since $P=\left(4,5\right)$ and $Q=\left(4,7\right)$, side $PQ$ is parallel to the y-axis and has a length of $2$. Since $P=\left(4,5\right)$ and $R=\left(6,5\right)$, side $PR$ is parallel to the x-axis and has a length of $2$. Therefore, triangle $PQR$ is a right isosceles triangle, where $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ has measure $90^{\circ }$ and $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ and $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ each have measure $45^{\circ }$. It follows that if the measure of $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ is $t^{\circ }$, then $t=45$. Since $L=\left(4,5\right)$ and $M=\left(4,7+k\right)$, side $LM$ is parallel to the y-axis and has a length of $k+2$. Since $L=\left(4,5\right)$ and $N=\left(6+k,5\right)$, side $LN$ is parallel to the x-axis and has a length of $k+2$. Therefore, triangle $LMN$ is a right isosceles triangle, where $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ has measure $90^{\circ }$ and $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ and $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ each have measure $45^{\circ }$. Of the given choices, only ${\left(90-t\right)}^{\circ }$ is equal to $45^{\circ }$, so the measure of $PARS{E}_{E}RROR:Entit{y}^{\prime }an{g}^{\prime }notdefined,line1,column83(<string>,line1)$ is $(90-t{)}^{\circ }$.