Question

如图所示,∠AOC是一条直线,OD平分∠AOB,OE在∠BOC内,∠BOE=1/4∠EOC,∠DOE=60°,

如图所示,∠AOC是一条直线,OD平分∠AOB,OE在∠BOC内,∠BOE=1/4∠EOC,∠DOE=60°,求∠EOC度数

Answer 1

∠EOC+∠AOD=180°-∠DOE=120°

∠BOE=60°-∠AOB/2

∠BOE=∠EOC/4

60°-∠AOB/2=∠EOC/4

240°-2∠AOB=∠EOC

240°-4∠AOD=∠EOC

240°-3∠AOD=∠EOC+∠AOD

240°-3∠AOD=120°

∠AOD=40°

∠EOC=120°-40°=80°