a. N is the incenter of ABC because it is the point of concurrency of the three angle
bisectors. So, by the Incenter Theorem, ND = NE = NF.
Step 1 Solve for x.
ND = NE
Incenter Theorem
5x - 1 = 2x + 11
* = 4
Substitute.
Solve for x.
Step 2 Find ND (or NE).
ND = 5x - 1 = 5(4) - 1 = 19
So, because ND = NF, NF = 19.