Question

OC,OD,OE是角AOB内的射线,OD平分角AOB,OC平分角BOD,角DOE=三分之一角AOE,若角COE=45度,

Answer 1

∵OD平分∠AOB

∴∠AOD＝∠BOD＝1/2∠AOB

∵OC平分∠BOD

∴∠COD＝1/2∠BOD＝1/4∠AOB

∵∠DOE＝1/3∠AOE

∴∠AOE＝3∠DOE

∴∠AOE+∠DOE＝∠AOD

∴4∠DOE＝∠AOD

∴∠DOE＝1/4∠AOD＝1/8∠AOB

∴∠COE＝∠COD+∠DOE＝1/4∠AOB+1/8∠AOB＝3/8∠AOB

∴3/8∠AOB＝45

∴∠AOB＝120°

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