Answer
M=60 degrees
N=60 degrees
Work Step by Step
Since MNP is an isosceles triangle, we know that angles P and N are congruent. Since MQ and QP are congruent, we know that small angle P (QPM) and M are congruent. Since QP and NP are congruent, second small angle Q (PQN) and angle N are congruent.
Thus, we find:
$$2N+QPM=180 \\ 2N+M = 180 \\ 2M+ MQP=180 \\ QPM+MQP+M=180$$
Using these equations and the triangle congruence theorems, we find that M is equal to:
$$ M=60 ^{\circ}$$
Thus, it follows:
$$ 2N+60 =180 \\ N = 60^{\circ}$$
