the damage is not from fish bites since it is spreading, and he is all by himself.
But he wasn't by himself when the damage was done. Fin rot is a secondary infection to wounds. He most likely got beat up by somebody. How many angels do you have in what size tank now compared to before the new fish were introduced?
What filter do you have?
there is a white edge between the good and bad parts
This is the sign of infection. That white edge is the frontline of the infection. If you are certain of yourself with handling fish, put stress coat on your hands and if there is enough finnage without getting too close to the body, cut the infected areas off (just past the white edge) with a clean pair of sharp scissors. Soak the scissors in bleach/water solution for 30 minutes, then soak in heavily dechlorinated water before using. Use Bio Bandage, made by Hikari to put over the infected areas and the areas that you cut. Needless to raise temp. That may progress infection, so lower it to 78 degrees...slowly. If you decide not to cut the bad areas of the fins, then it may just take a bit longer to heal.
You must get the nitrates down in the main tank at least to if not below 30ppm. Cut back on feeds...what fish can eat in a two minute time period per day three days a week. Do 10% water changes three times a week until nitrates are at desired level. You can use a denitrate filter media such as Phos-X in the filter to help absorb excess nitrate. Once nitrates are safe, up feeds to every other day, but stick to the same time period. Best divided into two or more feeds throughout the day. Maintain filter...rinse bio media in used tank water, clean out mechanical parts, hoses and tubes. Refresh carbon every two weeks until nitrates are lowered. Then go back to once a month as normally recommended. Good luck.
As mentioned before, the fins can grow back unless the nerve endings were damaged which are right at the base of where the fin meets the body. These areas generally don't grow back, but all the other areas can.
Angels are cichlids and are very territorial as they grow. Typically, it is recommended not to have more than a pair per 20 gallons and each pair should be introduced together and close to any other introductions of other pairs and should all be of about the same size. Once matured, they rarely accept other angels in their territory. I'm suspecting the new fish may have challenged this angel over territory. Usually it's the current territorial holder that wins the battle, but not all the time.
There is a slight possibility the angel may never be accepted back into the main tank, but first lets see if we can heal him up
