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.