Final answer:
The connective tissue layer surrounding individual muscle fibers is the endomysium, which works with other layers like the epimysium and perimysium to support and nourish the muscle.
Step-by-step explanation:
The connective tissue layer that surrounds individual muscle fibers, consisting of a basal lamina and reticular fibers, is called the endomysium. This thin connective tissue layer provides support by encasing muscle fibers within fascicles and supplying them with essential nutrients through the extracellular fluid. The endomysium is part of a network of connective tissue layers including the epimysium which surrounds the entire muscle and the perimysium which encases the bundles of muscle fibers.