∵AB=AC，∠A=30°（已知）∴∠ABC=∠ACB= 1 2 ×(180°?30°)=75°∵DE垂直平分AC，∴AD=CD；∴∠A=∠ACD=30°，∴∠BCD=∠ACB-∠ACD，∴∠BCD=45°；故答案为：45°．
