Question

已知OM是角AOB的平分线,OC是角BOM的平分线,ON是角BOC的平分线,若角AOC等于78度,求

Answer 1

∵OM,OC,ON分别平分∠AOB,∠BOM,∠BOC

∴∠AOM=∠BOM=1/2∠AOB

∠BOC=∠COM=1/2∠BOM

∠BON=∠CON=1/2∠BOC

∴∠COM=1/2∠AOM

∠CON=1/4∠AOM

不妨设∠AOM=x

则：∠COM=1/2x

∠CON=1/4x

∵∠COM+∠AOM=∠AOC

∴1/2x+x=78

解得：x=52

∴∠MON=∠COM+∠CON=1/2x+1/4x=26+13=39°