Question

已知OE是∠BOC的平分线,OD为∠AOC的平分线，且AOB=150°，求∠DOE的度数

Answer 1

∵OE是∠BOC的平分线,OD为∠AOC的平分线
∴∠EOC=∠BOC/2、∠COD=∠AOC/2
∴∠DOE=∠EOC+∠COD
=∠BOC/2+∠AOC/2
=(∠BOC+∠AOC)/2
=∠AOB/2
∵∠AOB=150°
∴∠DOE=150°/2=75°

Answer 2

∠DOE=∠DOC+∠COE
=(2∠DOC+2∠COE)/2
=(∠AOC+∠COB)/2
=∠AOB/2
=150°/2
=75°