△ABC中,∠BAC:∠ACB:∠ABC=4:3:2,且△ABC≌△DEF,则∠DEF=_度.
问题描述:
△ABC中,∠BAC:∠ACB:∠ABC=4:3:2,且△ABC≌△DEF,则∠DEF=______度.
答
设∠BAC为4x,则∠ACB为3x,∠ABC为2x
∵∠BAC+∠ACB+∠ABC=180°
∴4x+3x+2x=180,
解得x=20
∴∠ABC=2x=40°
∵△ABC≌△DEF
∴∠DEF=∠ABC=40°.
故填40.