设∠BOC=X
∵∠COD=Y
∠AOB :∠BOC=2 :1
∠COD:∠DOE=1 :2
∴∠AOB=2X,∠DOE=2Y
又∵∠AOE=∠DOE+∠DOC+∠BOC+∠AOB,∠AOE=150°
∴X+2X+Y+2Y=150°
即X+Y=50°
∴∠BOD=∠DOC+∠BOC=X+Y=50°
设∠BOC=X
∵∠COD=Y
∠AOB :∠BOC=2 :1
∠COD:∠DOE=1 :2
∴∠AOB=2X,∠DOE=2Y
又∵∠AOE=∠DOE+∠DOC+∠BOC+∠AOB,∠AOE=150°
∴X+2X+Y+2Y=150°
即X+Y=50°
∴∠BOD=∠DOC+∠BOC=X+Y=50°