Question

已知射线OC是角AOB内任意一射线,OE是角AOC的角平分线,OF是角COB的角平分线,若角EOF=64度,求角AOB的度数

Answer 1

∠EOF=∠EOC+∠COF
OE是角AOC的角平分线,所以∠AOE=∠EOC
OF是角COB的角平分线,所以∠COF=∠FOB
∠AOB=∠AOE+∠EOC+∠COF+∠FOB=∠EOC+∠EOC+∠FOB+∠FOB=2（∠EOC+∠COF）
=2∠EOF=2×64=128°