因为,AD = DE ,
所以,∠AED = ∠A ；
因为,DE = BE ,
所以,∠BDE = ∠DBE = (1/2)∠AED = (1/2)∠A ；
因为,BC = BD ,AB = AC ,
所以,∠BDC = ∠C = (1/2)(180°-∠A) = 90°-(1/2)∠A ；
因为,∠BDC = ∠A+∠DBE ,
所以,90°-(1/2)∠A = ∠A+(1/2)∠A ,
解得：∠A = 45° .