Welcome to the forum!
Like fishkies said...your angel fish will eventually get too big for the fish bowl. That whole "fish grow to the size of their environment" saying is actually partially a myth. Fish growth can be stunted by bad water conditions, but this will cause the fish harm and early death.
In good clean water a fish will continue to grow to it's full size.
Next, angel fish are tropical fish. They need a nice warm stable temperature, so tropical fish need a heater. Fish are cold blooded which means the temperature of their insides is the same as their surroundings...if it's too low or too high then their bodies can't function properly...for example they won't be able to digest their food correctly.
Lastly, filters are very important for several reasons. Fish have to excrete waste like all other animals, but unlike other animals they have to do it directly into the substance they breathe! In the wild this waste would be diluted by large quantities of water, and would be eaten by bacteria so it doesn't harm the fish. The reason that fish tanks have filters is to give those bacteria a good place to grow so the fishes gills won't be burned by the ammonia released from the fishes waste. The surface ripples caused by filters also help to increase the amount of oxygen in the water.
In the "New to the Hobby" section of the forum there are some very helpful threads. Read up on "cycling", which is what we call growing the bacteria colony that consumes ammonia and nitrites, and also the thread on tank maint.
The only fish that can really live in a "bowl" for a long period of time is the Betta. This is because Bettas have very special adaptions that let them breathe air, and survive in smaller quantities of water than other fish. Even they need clean water (frequent water changes) and should at least have heaters to maintain a stable temperature.
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