Final answer:
The cytoskeleton, composed of microfilaments, intermediate filaments, and microtubules, provides the necessary structural support and flexibility to a cell.
Step-by-step explanation:
The component that provides structural support, strength, and flexibility to the cell is the cytoskeleton. The cytoskeleton is composed of microfilaments, intermediate filaments, and microtubules. These structures form a matrix within the cytoplasm that not only supports the cell's shape but also aids in the transport of materials within the cell and anchoring of organelles. Microfilaments, in particular, are part of the actin cortex that lies just beneath the plasma membrane contributing to cell's mechanical properties. The endoplasmic reticulum (ER), which includes the rough ER studded with ribosomes for protein synthesis and the smooth ER involved in lipid synthesis, is a separate structure that is continuous with the nuclear membrane and plays other roles within the cell.