Question

射线OC和OD把角AOB分成角AOC:角COD:∠DOB=3:5:4③OM,ON分别是∠AOD和∠COB的平分线且∠MO

Answer 1

由已知可得

∠AOD=(3+4)/(3+4+5)∠AOB=（7/12）∠AOB

∠BOC=(4+5)/(3+4+5)∠AOB=（3/4）∠AOB

因为OM平分∠AOD

ON平分∠BOC

所以∠MOA=1/2∠AOD=(1/2)×(7/12)∠AOB=(7/24)∠AOB

∠BON=1/2∠BOC=(1/2)×(3/4)∠AOB=（3/8）∠AOB

∠MON=∠AOB-∠BON-∠MOA

=∠AOB-(7/24)∠AOB-(3/8)∠AOB

=（1/3）∠AOB

因为∠MON=21°

所以∠AOB=3∠MON=63°