The two barely interact during the killing game due to Rantaro's early death.
There are some parallels between Angie and Rantaro's personalities. Both are able to stay calm while everyone else may be stressed, and can take control of a situation, both in their own ways. The two also have somewhat similar talents; Angie is an artist while Rantaro is an adventurer. Both are talents that are often solitary activities. Both can also be thought of in a spiritual sense, and as good activities for self-discovery.
In Chapter 3, Angie makes effigies of the dead students, Rantaro included.
While the two have some similarities, they also have many differences that compliment each other. Angie has an upbeat, outgoing and playful personality while Rantaro has a relaxed yet somewhat-serious personality. Angie is very confident in herself (and Atua), while Rantaro at times seems to be unsure of himself. Both occasionally say things that make others wonder what they mean, but in Rantaro's case it usually comes off as mysterious, and in Angie's, just eccentric. It's these contrasting personalities, as well as the few similarities between the two that lead its fans to believe they would have a good dynamic.
In addition, their personalities can be expressed through their outfits, which go together pleasantly. Angie's bright yellow jacket, showing her cheerful personality, contrasts with Rantaro's dark colours themed outfit, showing his cool nature. Angie's jacket is also analgous with Rantaro's yellow-green hair.
In the Danganronpa fandom, it is a common joke about how Rantaro is an avocado due to the colour of his hair. In Angie's report card, it states that she likes avocados, which some people jokingly interpret as Angie likes Rantaro. This connection caused some people to start shipping Amanaga. Occasionally people claim the ship is canon due to Angie's liking of avocados, but it most often is not in seriousness. Some people say that Angie might eat Rantaro (an avocado) and is the true killer behind his death.