∠ADB = 72° (isosceles triangle BAD)
∠BAD = 36° (sum of angles in triangle BAD)
∠ACB = 36° (isosceles triangle ABC)
∠ABC = 108° (sum of angles in triangle ABC)
∠DCB = 36° (angle subtraction)
∠BDC = 108° (sum of angles in triangle BDC)
Since ∠DBC = ∠BCD, triangle BCD is isosceles.