This patent relates to a machine that automatically assembles, inspects, and packages disposable prophylaxis angles. The machine includes a movable table including a plurality of fixtures on which angle components are assembled and the assembled angles are inspected. The movable table is surrounded by a number of stations, each of which performs a different operation of the assembly and inspection procedure. Feeders automatically supply the angle components to their respective stations for assembly. Angles that are incorrectly assembled are automatically rejected. Properly assembled angles are automatically sealed in individual bags. Individually bagged angles are counted into batches by the machine and automatically sealed into cartons.