∵BD是角ADC的平分线,CD是角ACE的平分线
∴∠ABD=∠CBD,∠ACD=∠EDC
∵∠A+∠ABD=∠D+∠ACD
∴2∠A+2∠ABD=2∠D+2∠ACD
∵∠ACE=∠ABC+∠A
∴2∠A+∠ABC=2∠D+∠ACE=2∠D+∠ABC+∠A
∴∠A=2∠D