如图,在△ABC中,AB=AC,∠ABC=40°,BD是∠ABC的平分线,延长BD至E,使DE=AD,连接CE,则∠ECA的度数为_.
问题描述:
如图,在△ABC中,AB=AC,∠ABC=40°,BD是∠ABC的平分线,延长BD至E,使DE=AD,连接CE,则∠ECA的度数为______.
答
在BC上截取BF=AB,连接DF,∵BD是∠ABC的平分线,∴∠ABD=∠FBD,在△ABD和△FBD中,AB=FB∠ABD=FBDBD=BD,∴△ABD≌△FBD(SAS),∴DF=DA=DE,∠A=∠DFB,又∵AB=AC,∴∠ACB=∠ABC=40°,∴∠A=180°-∠ACB-∠...