Question

如图，∠AOB＝∠COD＝90⁰,OC平分∠AOB，∠BOD＝3∠DOE。试求 ∠COE的度数。

Answer 1

解：∵∠AOB＝90⁰，OC平分∠AOB
∴∠BOC＝∠AOB＝45⁰                          
∵∠BOD＝∠COD-∠BOC＝90⁰-45⁰＝45⁰
             ∠BOD＝3∠DOE                                      
∴∠DOE＝15⁰                                                                        
∴∠COE＝∠COD-∠DOE＝90⁰-15⁰＝75⁰   

根据角平分线的定义先求∠BOC的度数，即可求得∠BOD，再由∠BOD=3∠DOE，求得∠BOE．