Question

如图,已知:∠AOC与∠AOB之和是180°,OM、ON分别是∠AOC、∠AOB的平分线,且∠MON=40°,试求∠AO

Answer 1

∵∠AOB＋∠AOC＝180°

又∵∠AOM＝½∠AOC ∠AON＝½∠AOB

∴∠AOM＋∠AON＝½（∠AOB＋∠AOC）＝90°

∵∠MON＝∠AOM－∠AON＝40°

∴∠AOM＝65° ∠AON＝25°

∴∠AOC＝130° ∠AOB＝50°