From the rotation angle AP=AP'=3, P'B=PC=5, and the angle P'AP=60 degrees.

So the triangle AP'P is an equilateral triangle.

So the angle APP'=60 degrees, PP'=AP=AP'=3.

Because the square of PP '+BP = the square of 3+the square of 4 = the square of 5 = the square of P 'B.

So the triangle P'PB is a right triangle.

So the angle P'PB=90 degrees.

So angle APB= angle APP'+ angle P'PB=60+90= 150 degrees.