∵OM平分∠AOB，ON平分∠COD
∴∠AOM=∠MOB，∠CON=∠DON
又∵∠MON=50°，∠BOC=10°
则∠MON=∠MOB+∠CON+∠BOC=50°=∠AOM+∠DON+10°=50°
∴∠AOM+∠DON=40°
∴∠AOD=∠AOM+∠DON+∠MON=40°+50°=90°．
故答案为90°．