Question

已知射线OC,OD,OE分别是叫AOB的平分线,三等分线和四等分线（OE与OC不重合）,且角DOE=10度,求角AOB的

Answer 1

设∠AOB＝4α

则有：∠BOD＝4α/3或∠BOD＝8α/3

①当∠BOD＝4α/3时,∠BOE＝α

∴∠DOE＝∠BOD－∠BOE＝10°

4α/3－α＝10°

α/3＝10°

α＝30°

∠AOB＝4α＝4×30°＝120°

②当∠BOD＝8α/3时,∠BOE＝α

∴∠DOE＝∠BOD－∠BOE＝10°

8α/3－α＝10°

5α/3＝10°

α＝6°

∠AOB＝4α＝4×6°＝24°