Final answer:
The amoeba ingests food particles through the process known as phagocytosis, which is a type of endocytosis, leading to digestion within a lysosome and waste excretion by exocytosis.
Step-by-step explanation:
The amoeba is ingesting food particles through the process of phagocytosis. Phagocytosis is a type of endocytosis, a cellular process in which the amoeba extends pseudopodia around the food particles to engulf them. The resulting food vesicle merges with a lysosome, whose hydrolytic enzymes digest the food. The undigested waste is then expelled from the cell by exocytosis. This process is an essential part of how amoebas and many other unicellular organisms obtain nutrition.