Angie, Kaede, and Rantaro rarely have interacted with each other, likely because of Kaede's and Rantaro's early death's. Although they haven't interacted much neither of them are shown to be on bad terms with each other.
In Rantaro's case he seemed to find Kaede cool, because of her leader role among the other participants of the Killing School Semester. Kaede, later was framed to be Rantaro's murderer and got falsely executed for Rantaro's death.
It was revealed in Chapter 6 that Tsumugi Shirogane merely framed Kaede for Rantaro's death, to get her out of the way. Since she considered both Rantaro and Kaede a burden for the Killing School Semester.
In Angie's and Kaede's case. Angie or Kaede have barely interacted with each other. At the same time, Rantaro and Angie rarely and barely interacted with each other. But there are some parallels between Angie and Rantaro's personalities, both are able to stay calm when everyone else may be stressed and can take control of a situation, both in their own ways.
Amanagamatsu is a rare-pair among the Danganronpa fandom. The ship sailed due Rantaro's, Angie's and Kaede's different personalities. Rantaro’s high and positive opinion on Kaede helped the ship status grow. In Angie's report card it's also mentioned that she likes avocados and a huge part of the fandom jokes about Rantaro being an avocado because of his hair color. Nonetheless, Amanaga, Amamatsu, and Yonamatsu are all a bit more popular as separate ships and not as poly/full one. There's also not that much fan art depicting the three.
Otherwise the ship easily gets overshadowed by far more popular ships. For Angie being, Shironaga and Shinnaga. For Kaede being, Irumatsu, Saimatsu, and Nursery Rhymes. And lastly, for Rantaro being, Amaguji, Amasai, Oumami, and Amamiibo.
- Amamatsu refers to the ship just between Kaede and Rantaro
- Amanaga refers to the ship just between Angie and Rantaro
- Yonamatsu refers to the ship just between Angie and Kaede