Desmos Graphing Calculator

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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

Triangles PQR and LMN are graphed in the $xy$-plane. Triangle PQR has vertices P, Q, and R at $(5,2)$, $(5,4)$, and $(7,2)$, respectively. Triangle LMN has vertices L, M, and N at $(5,2)$, $(5,4+k)$, and $(7+k,2)$, respectively, where $k$ is a positive constant.

If the measure of $\angle Q$ is $t^{\circ }$, what is the measure of $\angle N$?

A

$(90-(t-k){)}^{\circ }$

B

$(90-(t+k){)}^{\circ }$

C

$(90-t{)}^{\circ }$

D

$(90+k{)}^{\circ }$