如图,点O是△ABC的内切圆的圆心,若∠BAC=70°,则∠BOC=_.

问题描述:

如图,点O是△ABC的内切圆的圆心,若∠BAC=70°,则∠BOC=______.

∵点O是△ABC的内切圆的圆心,
∴∠OBC=

1
2
∠ABC,∠OCB=
1
2
∠ACB,
∴∠OBC+∠OCB=
1
2
(∠ABC+∠ACB),
=
1
2
(180°-∠A),
=55°,
∴∠BOC=180°-(∠0BC+∠OCB),
=180°-55°,
=125°.
故答案为:125°.