Question

如图,已知△ABC中,∠ABC,∠ACB的平分线交与点O,过点O作EF//BC交与AB于点E,交AC于点F.

Answer 1

1、∠AEF=∠ABC,∠AFE=∠ACB,∠EOB=∠EBO=∠OBC,∠FOC=∠OFC=∠OCB

2、∠A=180°-∠ABC-∠ACB=40°

∵∠OBC=∠ABC/2,∠OCB=∠ACB/2

∴∠BOC=180°-(∠ABC+∠ACB)/2=110°

3、∵∠A=180°-∠ABC

∴(180°-∠A)/2=180°-∠BOC

即∠BOC=90°+∠A/2