moshe rabenu

Question

if Moshe was 80 when he came before Paroh, then there was a year of Mackot, and wandered 40 years in the dessert, why is it tha we say that he died at 120 when in actuality that adds up to 121 years? i thought that maybe he had passed his 120th birthday, therefore having entered the 121st year of his life, but thats not either possible considering he died on his birhtday. thank you for clarifying and explaining! ao