The first thing you should know in this case is that a circumference has a total measure in 360 degrees.
We have then that the formula to find EG in this case is:
EG + GF + FE = 360
We cleared EG:
EG = 360-GF-FE
We substitute the values:
EG = 360-83-66
EG = 211
Answer
EG = 211 degrees.
