Question

these figures are congruent. what is m∠m?

Explanation:

Step1: Recall congruent - figure property

Congruent figures have equal corresponding angles.

Step2: Identify corresponding angles

In the two congruent right - angled triangles, $\angle M$ corresponds to $\angle C$.

Step3: Determine the measure of $\angle C$

From the first triangle, $m\angle C = 36^{\circ}$.
Since $\angle M$ and $\angle C$ are corresponding angles of congruent triangles, $m\angle M=m\angle C$.

Answer:

$36$