Question

如图,已知∠ABC＋∠ACB=110°,BO、CO分别是∠ABC和∠ACB的平分线,EF过点O与BC平行,则∠BOC=_

Answer 1

∵在△ABC中BO、CO分别是∠ABC和∠ACB的平分线,

∴∠OBC=0.5∠ABC,∠OCB=0.5∠ACB.

∴∠OBC+∠OCB=0.5（∠ABC＋∠ACB）

又∵∠ABC＋∠ACB=110°

∴∠OBC+∠OCB=0.5（∠ABC＋∠ACB）=55°

∴在△OBC中,∠BOC=180°-（∠OBC+∠OCB）=125°