QM = QN = QP

But QP = AB = MN (they are lengths of the square)

So QM = QN = MN

So triangle QMN is equilateral, each with angle 180 / 3 = 60 degrees (the / symbol is a symbol for divide)

Let lines PQ and MN meet at K.

Angle QMK (same as angle QMN) is 60 degrees. Angle QKM is 90 degrees. So angle MQK is 180 - 90 - 60 = 30 degrees.

Now, remember that QM = QP, is triangle MQP is isosceles, with angle MQP = angle MQK = 30 degrees.

Angle QMP and angle QPM must total 180 - 30 = 150 degrees. Since both angles are the same value, then angle QPM = 150 / 2 = 75 degrees.

Similarly, angle QPN = 75 degrees (by a similar method).

Therefore, angle MPN = 75 + 75 = 150 degrees.