Question

Line DF bisects angle EDG. Find the value of x. Line EF has 9x+114. Line FO has 15x. angle FDG has 32 degrees.

Answer 1

No idea where O is, but if you meant FG=15x, then since FDG = FDE, FE=FG, so

9x+114 = 15x
4x = -114
x = -26

Answer 2

Actually, the above is true only if DF=DG.

I think there's something missing here.