Final answer:
The Rough Endoplasmic Reticulum (RER) is responsible for the synthesis and packaging of proteins, which are then transported to their destinations within the cell or exported.
Step-by-step explanation:
The organelle responsible for the synthesis and packaging of proteins is the Rough Endoplasmic Reticulum (RER). The RER is covered with ribosomes, where proteins are synthesized. These proteins are then transported from the RER in transport vesicles. Following synthesis, proteins may undergo modification and are directed to their proper destinations, such as the Golgi apparatus for further processing, the cell membrane, or for export from the cell. While the Golgi apparatus plays a crucial role in modifying, sorting, and packaging these proteins, it does not synthesize them, and the Smooth Endoplasmic Reticulum (SER) is involved in lipid synthesis and detoxification processes but not in protein synthesis.