Line DF bisects angle EDG. Find FG. The diagram is not drawn to scale.

Even if a diagram is not given, if you visualize it, EDG forms a right triangles with a bisector line DF. FG is then the lower half of segment EFG. To determine FG, use trigonometric functions like sine, cosine or tangent to relate the sides. For FG, you could use

tan ∅/2 = FG/DG

FG = DG tan (∅/2)

The angle is denoted as ∅/2 because of the angle bisector. DG is the base of the right triangle.