Question

如图,直线ab,cd相交于点o.oe平分角aod,

Answer 1

∵∠AOD：∠DOE＝4：1 ∴∠AOD＝4∠DOE ∵OE平分∠BOD ∴∠BOE＝∠DOE ∴∠BOD＝2∠DOE ∵∠AOD+∠BOD＝180 ∴4∠DOE+2∠DOE＝180 ∴∠DOE＝30 ∴∠AOD＝4∠DOE＝120 ∵∠BOC与∠AOD为对顶角 ∴∠BOC＝∠AOD＝120 ∵OF平分∠BOC ∴∠BOF＝∠BOC/2＝60 ∴∠AOF＝180-∠BOF＝180-60＝120°