如图,在ABC中,角ABC,角ACB的角分线交于点O试探究角A与角BOC之间具有怎样的数量关系？为什么？

∠BOC＝90+1/2∠A证明：延长BO交AC于D∵BO平分∠ABC∴∠ABO＝1/2∠ABC∴∠BDC＝∠A+∠ABO＝∠A+1/2∠ABC∵CO平分∠ACB∴∠ACO＝1/2∠ACB∴∠BOC＝∠BDC+∠ACO＝∠A+1/2（∠ABC+∠ACB）∵∠ABC+∠ACB＝180-∠A∴∠BOC＝∠A+1/2（180-∠A）＝90+1/2∠A