Question

AO垂直于BO,OC为一条射线..OM平分角AOC,ON平分角BOC,射线OC在角AOB外部时,求角MON的度数?

Answer 1

∵AO⊥BO

∴∠AOB＝90

∵∠BOC＝∠AOB+∠AOC,ON平分∠BOC

∴∠CON＝∠BOC/2＝（∠AOB+∠AOC）/2

∵OM平分∠AOC

∴∠COM＝∠AOC/2

∴∠MON＝∠CON-∠COM＝（∠AOB+∠AOC）/2-∠AOC/2＝∠AOB/2＝45°