The figure appears to be a rectangle and its opposite sides are parallel.
With this condition, ∠FDB and ∠EBG should be alternating angles same with ∠BED and ∠DFE. Under the rules of alternate angles, the two angles should be equal.
Therefore, ∠FDB = ∠EBG and ∠FDB = 27°
∠EBG should also be equal to 27°
The answer is 27°