In which cell organelles are proteins synthesized?

Proteins are synthesized by non-membrane organelles. These are ribosomes. They can be found in the cytoplasm in free form or on the membranes of the cell and some organelles. For example, ribosomes are found on chloroplasts and mitochondria. So they can synthesize the proteins they want, reducing the load on the nucleus. Mitochondria and chloroplasts also have their own DNA with RNA. Ribosomes are created using rRNA. In eukaryotic cells, they are created by the nucleolus. It is in the core. Prokaryotes create ribosomes directly on DNA structures in the cytoplasm.