Question

如图,角AOB=90度,角BOC=30度,角AOC=3角AOM,角BOC=3角BON,求角MON的度数.

Answer 1

①∠AOC=∠AOB+∠BOC=120º

∠MOB=∠AOB-∠AOM=∠AOB-1/3∠AOC=50º

∠BON=1/3∠BOC=10º

∠MON=∠MOB+∠BON=60º

②∠AOC=∠AOB+∠BOC=∠α+30º

∠MOB=∠AOB-∠AOM=∠AOB-1/3∠AOC=∠α-1/3(∠α+30º)=2/3∠α-10º

∠MON=∠MOB+∠BON=2/3∠α

③∠BON=1/3∠BOC=1/3∠β

∠AOC=∠AOB+∠BOC=90º+∠β

∠MOB=∠AOB-∠AOM=∠AOB-1/3∠AOC=60º

④∠MON=2/3∠AOB