All three players have been involved in the first team this season, with striker Nangle scoring his first goal for the club against Colchester this month.
Academy manager Mick Leonard has congratulated the trio that are set to make the step up to the senior squad next season, but has warned them that the hard work has only just begun.
"Myself and (first-team manager) Chris Kiwomya made it quite clear that it's just a start for them," Leonard told the club's official website.
"They are back to square one and they will have to push themselves further and harder if they want to make a career in the game.
"It now means that we have had 10 players offered professional contracts since the academy's reintroduction, which is fantastic news for the programme."
Meanwhile, second-year scholars Liam Guest, James Randall, Mitchell Clarke, Kameron Campbell and Matthew Crust have all been released.