BE and CD are parallel
FD and GC are parallel
That implies that point G CANNOT be on the line BE.
If G were on the line BE then angle BGC (which is given as 82deg13min46sec) should equal angle GCD (which is indicated as 90degrees).
It really looks as if this is a "flawed" question.
That is, you are given invalid information for the purpose of understanding how you handle errors.
What data will you use and what information will you ignore?