Answer
$m\angle M$ is $90^{\circ}$, and $m\angle N$ is $90^{\circ}$.
Work Step by Step
If we know that $\angle M$ is supplementary to $\angle N$ and that they are congruent, then let's have $x$ be the measure of one angle and $2x$ be the measure of both angles. If we set $2x$ equal to $180$, then we have the measure of one of the angles:
$2x = 180$
Divide each side by $2$ to solve for $x$:
$x = 90$
$m\angle M$ is $90^{\circ}$, and $m\angle N$ is $90^{\circ}$.
