已知,∠AOB为直线,OE,OD,OC为射线,OC平分∠BOD,∠AOE :∠EOD=1:3,∠AOD-∠DOB=40°,求∠EOC的度数

因为,∠AOD+∠DOB = ∠AOB = 180° ,∠AOD-∠DOB = 40° ,所以,∠AOD = 110° ,∠DOB = 70° ；因为,∠AOE：∠EOD = 1：3 ,所以,∠AOE：∠AOD = ∠AOE：(∠AOE+∠EOD) = 1：(1+3) = 1：4 ,可得：∠AOE = (1/4)∠AOD ...