∵AE平分∠BAD，CF平分∠BCD∴∠BAE=∠EAD，∠BCF=∠DCF又∵平行四边形ABCD∴AD//BC，∠BAD=∠BCD∴∠DAE=∠AEB∴∠AEB=∠FCB∴AE//CF∴∠BCF+∠AEC=180°
