Final answer:
Enzymes that add phosphate groups to other enzymes to activate or deactivate them are called protein kinases, which perform the process of phosphorylation.
Step-by-step explanation:
The type of enzyme responsible for adding phosphate groups to other enzymes in order to activate or deactivate them is known as protein kinases. During this process, termed phosphorylation, a protein kinase transfers a phosphate group from a high-energy molecule like ATP to specific amino acids within a target protein, typically serine, threonine, or tyrosine. This addition of a phosphate group often induces a change in the shape of the protein, which can turn its function on or off, acting as a regulatory mechanism within the cell.