Final answer:
The rough endoplasmic reticulum (RER) is the structure responsible for the synthesis of proteins that may be exported from the cell. Proteins synthesized on the RER are further processed and packaged in the Golgi apparatus before being exported from the cell.
Step-by-step explanation:
The structure responsible for the synthesis of proteins that may be exported from the cell is the rough endoplasmic reticulum (RER).
The RER is covered with ribosomes, giving it a rough appearance, and it transports materials through the cell. It synthesizes proteins in sacks called cisternae, which are designated for export or movement to different cell organelles like the Golgi body or insertion into the cell membrane but not to the cytoplasm.
The proteins synthesized on the RER enter the Golgi apparatus through Golgi vesicles, where they are further organized, modified, packaged, and tagged for export from the cell.