It may take a long time, but it is necessary. Please be patient. Remember to give points if you feel good ~ ~

Let ∠COE=∠EOF=a, ∠FOB=∠AOB=b, then ∠COF=2a, ∠FOA=2b (remember to draw a picture in your notebook and mark A and B).

( 1)，∫≈C = 100 BC‖OA

∴∠COF+∠CFO=2a+2b=80

∴a+b=40=∠EOB

(2) unchanged, the ratio is 1:2 for the following reasons:

∫BC‖OA

∴∠OBC=∠BOA=b ∠OFC=∠FOA=2b

So ∠ OBC: ∠ OFC = 1: 2.

(3) Existence, ∠OEC=40, for the following reasons:

∠∠OBA = 180-∠BOA- 100 = 80-b

OEC = 180-∠COE- 100 = 80-a

When a=b, ∴∠oba =∠OEC.

∫In△COF， 180= 100+2a+2b

When a = b, a+b=40, that is, a=b=20.

∴∠OEC=80-a=80-20=60

The above is my answer, I hope it will help you, thank you.