Final answer:
Lysosomes are membrane-bound organelles with an acidic environment that contain digestive enzymes used to break down phagocytized material and other cellular debris.
Step-by-step explanation:
The organelle with an acidic pH and digestive enzymes used to digest phagocytized material is the lysosome. Lysosomes are membrane-bound organelles that contain approximately 40 hydrolytic enzymes, such as lipases, proteases, and nucleases, which break down various organic polymers. They are involved in processes like phagocytosis and autophagy, aiding in the digestion of foreign materials, worn-out organelles, and cell debris. Moreover, they play a crucial role in the cell's defense by destroying pathogens. The acidic environment inside the lysosome is maintained through proton pumps in the lysosome membrane, which is vital for the optimal functioning of these enzymes.