Solution to the first problem: Because OC is the bisector of angle AOB, angle AOC= angle BOC.

Because angle COD= angle EOD+ angle BOD= angle BOE= angle BOC+ angle BOD.

So angle EOD= angle BOC= angle AOC.

Angle AOE= Angle AOC+ Angle BOC+ Angle EOD+ Angle BOD.

=3 angle AOC+ angle BOD= 140 degrees

Angle COD= Angle BOD+ Angle BOC= Angle BOD+ Angle AOC=90 degrees.

Solve equation (1)3 Angle AOC+ Angle BOD= 140 degrees.

(2) Angle BOD+ Angle AOC=90 degrees.

The angle BOD=65 degrees is obtained.

Answer to the second question: From the question, we know that AOM=COM BON=CON.

(1) BOC = bon+con = 2bon = 2con = 50 degrees, so BON=CON=25 degrees.

AOB=AOM+BOM=COM+BOM=BOC+BOM=50 degrees +BOM=80 degrees.

So BOM=30 degrees

MON=BOM+BON=30+25=55 degrees.

(2)

BOC=BON+CON=2BON=2CON=b so BON=CON= 1/2b.

AOB = AOM+BOM = COM+BOM = BOC+BOM = b+BOM = a

So BOM=a-b

MON = BOM+BON = a-b+ 1/2b = a- 1/2b