∵OM,ON分别是∠AOC与∠AOB的平分线
∴∠AOB=2∠AON,∠AOM=1/2∠AOC
∵∠MON=40°
∴∠AON=∠AOM-40°
∴∠AOB=2∠AON=2（∠AOM-40）=∠AOC-80°
又∵∠AOC与∠AOB的和是180°
∴∠AOB=180°-∠AOC=∠AOC-80°
2∠AOC=260°
∠AOC=130°
∴∠AOB=180°-130°=50°