Point P is a point in the square ABCD, connecting AP, BP, CP, DP. If △ ABP is an equilateral triangle, find the degree of ∠ cpd

Point P is a point in the square ABCD, connecting AP, BP, CP, DP. If △ ABP is an equilateral triangle, find the degree of ∠ cpd

Because ABCD is a square and △ ABP is an equilateral triangle, the angle PBC = angle DAP = 30 degrees, the angle APB = 60 degrees, the △ BCP and △ ADP are equilateral triangles, and the angle PBC = angle DAP = 30 degrees, the △ BCP and △ ADP are equilateral triangles, so the angle DPA = angle BPC = 75 degrees, so the angle cpd + angle BPC + angle DPA + angle APB = 360 degrees, the angle cpd = 150 degrees