Question

如图所示AOC为直线,OD是∠AOB的平分线OE在∠BOC内∠BOE=2/1∠EOC,∠DOE=72求∠EOC

Answer 1

∵OD是∠AOB的平分线
∴∠AOD=∠DOB=1/2∠AOB
∵∠BOE=1/2∠EOC
∴∠BOE=1/3∠BOC
∵∠AOB+∠BOC=180°
∠DOE=∠DOB+∠BOE
=1/2∠AOB+1/3∠BOC
=1/2AOB+1/3（180°-∠AOB）
=1/2∠AOB-1/3∠AOB+60°
=1/6∠AOB+60°
∴1/6∠AOB+60°=72°
1/6∠AOB=12°
∠AOB=72°
∴∠AOD=1/2∠AOB=36°
望采纳。