∠AOB=150度,OD为∠BOC的平分线,OE为∠AOD的平分线,∠COE=30°则∠AOD是多少度,∠COD是多少度

Question

∠AOB=150度,OD为∠BOC的平分线,OE为∠AOD的平分线,∠COE=30°则∠AOD是多少度,∠COD是多少度

Answer 1

因为你没有图,所以不太确定是哪一种.以下是以我画出的图所做的解题方法.
(1)在AB线上,点的顺序为ACEDB
假设∠EOD=x
∠BOD = ∠COD + x = 30 + x
∠AOE = ∠EOD = x
∠AOB = ∠AOE + ∠EOD + ∠BOD = x + x + 30 + x = 150
.:∠EOD = x = 40
.:∠AOD = 80,∠COD = 40 + 30 = 70
(2) 在AB线上,点的顺序为AECDB
假设∠COD = x
∠BOD = ∠COD = x
∠AOE = ∠EOC + ∠COD = 30 + x
∠AOB = ∠AOE + ∠EOC + ∠COD + ∠BOD = 30 + x + 30 + x + x = 150
.:∠COD = x = 30
.:∠AOD =∠AOE + ∠EOC + ∠COD = 60 + 30 + 30 = 120