AB=BC=PC, angle PBA= angle PCA.
Triangle PBA and triangle MCP with edges are congruent.
PA=PM, angle BAP= angle CPM.
Angle PAM= Angle PMA= Angle CPM+ Angle PCM
Then it is very simple to get the angle PAC=30 degrees.
For example, let the angles ABP=b, BAP=x and PAC = y.
Extend BP AC to point F.
Angle bfc =180-(a-b)-(120-a+b) = 60.
Look at the picture, x+y+b=60.
On the other hand, because the triangle PAM is isosceles and congruent.
X+b= angle PMA=y
y+y=60
Get y=30.