What is the role of the rough endoplasmic reticulum and the Golgi apparatus in protein transport within cells?

Firstly, during protein synthesis, the DNA is transcribed into mRNA in the nucleus, which then can move out of the nucleus into the cytoplasm. This is where translation occurs, where the mRNA is read and translated into a polypetide chain (a chain of amino acids) at a ribosome. The poplypetide chain then enters the rough endoplasmic reticulum, where translation continues and the protein is modified; sugar groups may be added to form glycoproteins. The modified proteins are then pinched of the rER into vesicles and transported to the golgi appartaus where the proteins are further modified. The protein is then pinched off the golgi apparatus in vesicles and leaves the cell through exocytosis.