如图,在三角形ABC中,角ABC,角ACB的平分线交于O(1)若角A=50度,求角BOC的度数;(2)设角A=n度(n为已知数),求角BOC的度数;(3)当角A为多少度时,角BOC=3角A

问题描述:

如图,在三角形ABC中,角ABC,角ACB的平分线交于O
(1)若角A=50度,求角BOC的度数;
(2)设角A=n度(n为已知数),求角BOC的度数;
(3)当角A为多少度时,角BOC=3角A

延长BO交AC于D,延长CO交AB于E∵∠A+∠ABC+∠ACB=180∴∠ABC+∠ACB=180-∠A∵BO平分∠ABC∴∠ABD=∠ABC/2∴∠BDC=∠A+∠ABD=∠A+∠ABC/2∵CO平分∠ACB∴∠ACE=∠ACB/2∴∠BOC=∠BDC+∠ACE=∠A+(∠ABC+∠ACB...