I have done lots of research and have some experience in taking care and breeding angles.
#1 as mgamer stated, it often takes the parents a try or 2 tto get it down right and they will usually eat the eggs.
#2 Often when you turn the lights out, the parents can not defend there eggs because they cant see and fight away the nocturnal predators (such as the pictus catfish).
#3 They make ALOT of babies. Sometime enough for a 75 gallon to be filled.
So there is alot to consider. When they hatch for the first week or so they stay on the surface attached. They slowly start becoming little fish and practice becoming free swimmers. You start feeding them baby brine shrimp once there little feeding sacks go away. You keep this up until there big enough to get crunched up flake (once they are about nickle size). You slowly mix it in with there baby brine shrimp. While there young you need to do a 25% water change everyday and make sure to get all the uneaten food of the bottom. Bare bottom tanks are better and makes it easier to clean. You need to feed them small amounts 3 times a day (morning, noon, night). Also make sure you separate the parents out of the tank with the babies about the time you can start seeing there fins taking shape as a angelfish. It will be heartbreaking as the parents will freak out looking for there babies. And this is only if you have the parents raise them. If you do the raising yourself then you need to make sure you have a air pump going over the eggs to simulate what the parents do with fanning the eggs. It is very interesting to see the young though, because they have traits from bouth the parents and can be very beautiful.
Also be careful of fungus on the eggs. The eggs will turn white if there dead or unfertilized and they will be white and fuzzy if they have fungus. Make sure the fungus eggs are removed because it can spread to the good eggs. This is the purpose of the parents fanning the eggs, to keep the fungus of them. There are products that can help with keeping the fungus away. Just let me know if you need help and have questions if and when you want to do it.
So think about it if you want to do it because it is ALOT of work.