The odds of having the eggs get past the first few days in a community tank is almost impossible. First, the angels themselves may or may not be good parents. most take a few tries to get it right and some never will, they end up eating their eggs every time. Even if the parents are good onek, the eggs may not last as parents will also eat their own eggs before they will let something else have the good meal, And lets not forget all the other tank inhabitants who just see angel eggs as a good meal.
This leaves you two choices, remove the other fish and hope that doing so doesn't cause the parents to freak and eat their eggs. There is still no guarantee they still wont even after they are the lone inhabitants. The other choice is to pull the eggs and hatch them elsewhere. You will need a small tank, airstone and pump, a heater and some methyl blue to prevent fungus. The blue should be removed via a 50% wc and a bag of carbon hung above the airstone when you see wigglers. You can cut that leaf at the stem and move them that way.
You will need to feed the fry live food for at least the first week after they go free swimming (absorb all their yolk sac) and then begin to mix in fry food to wean them off of the live. And it gets to be more work from there. It looks like you have a few 100 eggs there and if most hatch you will need at least one and more likely two 55 gal. tanks to raise the fry.
The one consolation in all this is that when angels first begin to spawn, they will do so more than once. They can actually go again in as few as 10 days but 2-3 weeks is more common. So if you can't move on things this time, you can get prepared for the next time if raising the fry is your goal.
Here is a picture of a 500+ fry spawned and then hatched out in a 2.5 gal.- these pictures and what follows is why I do not breed angels- way to many fry way to often