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=______.
答
∵点O是△ABC的内切圆的圆心,
∴∠OBC=
∠ABC,∠OCB=1 2
∠ACB,1 2
∴∠OBC+∠OCB=
(∠ABC+∠ACB),1 2
=
(180°-∠A),1 2
=55°,
∴∠BOC=180°-(∠0BC+∠OCB),
=180°-55°,
=125°.
故答案为:125°.