Final answer:
Phagocytes use lysosomes to digest engulfed particles.
Step-by-step explanation:
The organelle that phagocytes use to digest engulfed particles is the lysosome. Lysosomes are membrane-bound organelles that contain digestive enzymes. They play a major role in the activity of macrophages, which are a type of white blood cell that engulfs and destroys pathogens through a process called phagocytosis. In phagocytosis, the plasma membrane of the macrophage invaginates and forms a vesicle, which then fuses with a lysosome. The lysosome's hydrolytic enzymes then digest the engulfed pathogen.