试题

如图，∠AOB=120°，∠COD=20°，OE平分∠AOC，OF平分∠BOD，求∠EOF的度数．

解：∵∠AOB=120°，∠COD=20°
∴∠AOC+∠BOD=∠AOB-∠COD=120°-20°=100°
又∵OE平分∠AOC，OF平分∠BOD
∴∠EOC+∠DOF=

1

2

∠AOC+

1

2

∠BOD=

1

2

（AOC+∠BOD）=

1

2

×100°=50°
∴∠EOF=∠EOC+∠DOF+∠COD=50°+20°=70°
解：∵∠AOB=120°，∠COD=20°
∴∠AOC+∠BOD=∠AOB-∠COD=120°-20°=100°
又∵OE平分∠AOC，OF平分∠BOD
∴∠EOC+∠DOF=

1

2

∠AOC+

1

2

∠BOD=

1

2

（AOC+∠BOD）=

1

2

×100°=50°
∴∠EOF=∠EOC+∠DOF+∠COD=50°+20°=70°