The organelle responsible for degradation of material brought into the cell by endocytosis is the lysosome.

Here's why:

* Endocytosis: This is the process where cells engulf material from their external environment, packaging it into membrane-bound vesicles.

* Lysosomes: These are small, spherical organelles filled with powerful digestive enzymes. They act like the cell's recycling center.

When an endocytic vesicle fuses with a lysosome, the enzymes within the lysosome break down the ingested material (proteins, carbohydrates, lipids, etc.) into smaller components that can be reused by the cell.