∵△ABC是等边三角形，∴∠BAC=60°，∵D为BC的中点，∴AD⊥BC，∠DAC= 1 2 ∠BAC=30°，∵AE=AD，∴∠ADE= 180°?∠DAC 2 = 180°?30° 2 =75°，∴∠EDC=∠ADC-∠ADE=90°-75°=15°．故选A．
