There are two hypotheses regarding the origin of membranous organelles in eukaryotes. The first is that invaginations of membrane resulted in the formation of cellular organelles. The second is called the endosymbiotic theory which states that primitive prokaryotes lived as endosymbionts inside eukaryotes and subsequently evolved into organelles.
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Some evidence supporting the endosymbiotic theory is that the mitochondria and chloroplasts have their own genome, suggesting that these organelles were once their own organisms. In addition, mitochondria and chloroplasts have 70S ribosomes similar to prokaryotes, which suggests that organelles evolved from prokaryotes.