Question

如图所示,OM,OB,ON是∠AOC内的三条射线,OM、ON分别是∠AOB,∠BOC的平分线,∠NOC是∠AOM的三倍,

Answer 1

∵OM平分∠AOB

∴∠AOM＝∠MOB＝∠AOB/2

∵ON平分∠BOC

∴∠NOC＝∠BON＝∠BOC/2

∵∠NOC＝3∠AOM

∴∠BOC/2＝3∠AOB/2

∴∠BOC＝3∠AOB

∵∠BON-∠MOB＝20

∴∠BOC/2-∠AOB/2＝20

∴∠BOC-∠AOB＝40

∴3∠AOB-∠AOB＝40

∴∠AOB＝20

∴∠BOC＝3∠AOB＝60

∴∠AOC＝∠AOB+∠AOC＝80