Final answer:
The protective layer surrounding the cell membrane of euglenoids is called the pellicle. It is a flexible, protein-based structure that provides rigidity and strength to the cell.
Step-by-step explanation:
The protective layer made of rigid or elastic protein strips surrounding the cell membrane of euglenoids is called the pellicle. It is a flexible, protein-based structure that provides rigidity and strength to the cell, similar to a cell wall but more flexible. The pellicle can be seen as delicate parallel striations over the surface of the entire cell.