设∠ABD = X .（按题中的条件无法确定∠ABD,还要加个条件：AB=AC）
已知,AD = BD = BC ,可得：∠BAD = ∠ABD = X ；
已知,AB = AC ,BD = BC ,可得：∠ABC = ∠BCD = ∠BDC = ∠BAD+∠ABD = 2X ；
因为,∠BAD+∠ABC+∠BCD = 5X = 180° ,
所以,X = 36° ,即有：∠ABD = 36° .