Triangles P Q R and L M N are graphed in the xy -plane. Triangle P

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 $\angle P$ has measure $90°$ and $\angle Q$ and $\angle R$ each have measure $45°$. It follows that if the measure of $\angle Q$ is $t°$, 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 $\angle L$ has measure $90°$ and $\angle M$ and $\angle N$ each have measure $45°$. Of the given choices, only $\left(90-t\right)°$ is equal to $45°$, so the measure of $\angle N$ is $(90-t)°$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.