Question

如图，直线AB,CD相交于O，OE平分∠BOD，∠AOE=140°，求∠AOC的度数

Answer 1

∠AOE=140°，那么∠BOE=∠AOB-∠AOE=180°-140°=40°
OE平分∠BOD,所以∠BOE=∠EOD=40°
所以∠AOD=∠AOB-∠BOE-∠EOD=100°
所以∠AOC=∠COD-∠AOD=180°-100°=80°

Answer 2

∠BOE=∠DOE, ∠DOE+∠AOE+∠BOE=2∠DOE+∠AOE=180=140+DOE,所以∠DOE=40,
∠AOC=∠DOB=180-∠AOD=180-(AOE-DOE)=180-140+DOE=80°