设∠AOC=x，则∠BOC=2x，∴∠AOB=3x，∵OD平分∠AOB，∴∠AOD=∠DOB= 1 2 ∠AOB= 3 2 x，∴∠COD= 3 2 x-x=19°，∴x=38°，∴∠AOB=3x=114°．
∵∠AOD=∠BOD∴∠AOC+20°=∠BOC-20°∵∠BOC=2∠AOC∴∠AOC=40°∴∠AOB=∠AOC+∠COB=40°+80°=120°
