How would you determine input in a radial menu?

I add interactivity to actors in the game world by adding components which each house some specific functionality: Loot, Talk, Look, Use, and so forth. I store every interactable component in a TArray<Interactables>, and when the player hits Use, I draw one pie wedge for each element of the array, so the end result ends up looking something like . Where I’m stuck is figuring out how to actually register input from this- there is no mouse cursor, so I want to use mouse/analog stick movement alone to determine which pie slice should be active (and thus have its corresponding element in the array called when the player clicks), but I’m really running into trouble figuring out how- I know I can figure out how big each slice is by dividing 360/array.Num(), and I could try translating the input on the x + y axes from -1,1] to a degree measurement, but that sounds like a really clunky way to do it.