Board Thread:Naruto Discussions/@comment-26488946-20150612205152/@comment-681696-20150613005021

Legendary Super Saiya-Jin 4 wrote: It's because Sasuke and Madara awakened it on their own. Nagato is an Uzumaki who had the Rinnegan implanted into his eyes as child. He didn't start off with a Sharingan later unlock Mangekyo Sharingan and then Eternal Mangekyo Sharingan and finally Rinnegan.

Transplanted eyes have been shown to retain their original abilities after a transplant and Nagato had Madara's or to be more precise Izuna's eyes which had the sharingan and Eternal Mangekyou Sharingan.