A nice problem that combines geometry and algebra.
Let x be the smallest angle; then the angles are x, 5x, and 180 - 6x. Saying that each of these angles is acute gives you two inequalities (well, three, but the third one trivially follows from one of the others). In my calculations, these inequalities have two integer solutions. However, in one of them, 5x is not the greatest angle. This leaves one solution.