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The seventh answer to homework optimization mathematics
It is known that OE bisects the angle AOB and the angle AOE=30 degrees, so the angle EOB= AOE=30 degrees.

Angle BOD=20 degrees Angle AOD= Angle AOE+ Angle EOB+ Angle BOD=80 degrees.

Because OD bisects angle AOC, angle DOC= angle AOD=80 degrees.

Angle BOC= Angle BOD+ Angle DOC=20+80= 100 degrees.

Because the bisecting angle BOC, the angle COF= 100/2=50 degrees.

I hope it will help you, but I still hope to adopt it ~ ~