I've found that damaged fins heal at different rates depending on the species. So far I've observed damaged fins heal on a Mandarin Dragonet, Maroon Clownfish and the latest boo boo is my Yellow Tang. The Dragonet and Clownfish healed fairly quickly, less than a week for the Clown a bit longer for the Dragonet. Of course it depends on the extent of the damage as well. My Yellow Tang has had a relatively small section missing for well over a month now (near the lower end of the Dorsal Fin), just doesn't seem to want to close up. Looks like a small bite mark although he's more or less one of the tank bosses, maybe he got a little close to my Maroon's clutch of eggs, I dunno.
As far as Angelfish go, I have a Singapore (Vermiculated) and he's never had a damaged fin since I've had him, so I can't comment on how quickly an Angelfish might heal. Try to ensure your water quality is good, which we all do anyhow right? and chances are your dude will heal up fairly quickly. Other than that there's not much to do except observe. If he's swimming around normally and eating ok, should be no reason to be concerned, other than it doesn't look too nice.
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