∵∠AOB=90°，且∠AOC=30°，∴∠COB=∠AOB+∠AOC=90°+30°=120°，∵OM平分∠BOC，∴∠BOM= 1 2 ∠BOC=60°，∴∠AOM=∠AOB-∠BOM=30°，∵ON平分∠AOC，∴∠AON= 1 2 ∠AOC=15°，∴∠MON=∠AOM+∠AON=45°．∴∠MON的度数是45°．故答案为45°．
