I don't remember well, and I'm not sure if this is correct, but, I think the answer is This is beacuse ∠FCD are facing with ∠CDG meaning it would be a same side interior angle.
If you extend BF until it meets AG and consider the the triangle CD and the meeting point, then angle FCD is an interior angle.
If on the other hand it might just be the supplement of DCB which would make it neither. I can see why you want us to take a shot at it. That is a seat of my pants answer. If someone has a better reason, take that one.
