This question needs an auxiliary line, as shown in the figure.

Comment on BM, construct parallelogram BNDM, and connect AD.

BM = AC (known), and ND is translated from BM.

∴ND=AC

Ⅶ in △AMC and △DAN

ND=AC (confirmed)

Angle C= angle DNA

AN=MC (known)

∴△AMC≌△DAN (corner)

∴AN=AD (corresponding edge)

Angle 3= Angle 2 (corresponding angle)

In right triangle ACM, angle 1+ angle 2 = 180- angle C = 90.

∴ Angle 1+ Angle 3 = 90? Angle dam = 90.

∴ Angle AMD= Angle ADM=45 degrees.

BN‖MD again? ∴ Angle AMD= Angle BPM=45.

Finally solved ~ in fact, there are other ways.

Good luck ~