d. 19
Since DF bisects EDG, we know that the angles EDF and GDF are congruent. Additionally, since both EF and GF are perpendicular to their respective lines, and since both triangles EDF and GDF both share line segment DF as a common side, we know that triangles EDF and GDF are congruent to each other. Because they're congruent, we know that 9x + 114 is equal to 15x. So let's set the equality equation and solve for x.
9x + 114 = 15x
114 = 6x
19 = x
So the answer is "d. 19"
