A tank should be cycled before any fish goes into it. But, it looks like your stock is very light for the volume of water, so you can get away with it if you do about 40% water changes every day or two for the next 2-3 wks. The only way to know for sure if the tank is cycled is to get a test kit. You are cycled when ammonia and nitrite are at zero and nitrates shows up. The beneficial bacteria once established will break down ammonia and nitrite which are very toxic to fish. Nitrite is broken down to nitrate by these bacterias. Nitrate is no where near as toxic but can render health issue with prolong high level exposure. The simpliest way to get rid of nitrate is water changes and plants.
I have now had the water going for two weeks, and the angels are living.
Like I said, the main reason is the small fish size in a large fish tank. Just because they seem fine, doesn't mean they're fully healthy. Surviving doesn't mean thriving. Do your fish a favor and get a test kit. Don't treat them like disposable pets.