Finding the side length of a triangle type problem Find $x$ in the diagram

Man.. I bet this is really easy but I can't seem to figure out what to do. Law of cosines won't work because I don't know the angle across from $x$. Those two angles are the same, but I don't know how to make that useful. Help appreciated here for a geometry noob! Thanks a ton I really appreciate the help.

You can use angle bisector theorem, the angle bisector divides the opposite side such that their ratio is equal to ratio of other two sides , in your case,
6.4/8=(16-6.4)/x which gives x=12
