It is hard to imagine 80 as a small tank but it is i guess. let me tell you what i tell other people who ask me.
yes you can and it will probably do fine, at least for a while. but it will be a problem eventually. There is a lot you can get away with some of the time that would otherwise be disastrous. Now nobody here can say we run a perfect tank (people with glass fish tanks should not throw stones

) so we can only give advice based on experience or what we hear.
My advice, small tang at most.
Now if you decide to do it i will give you the other half of my advice (this is where experience pays off) this is what you need to watch for to tell when it is time (past time) to get a bigger tank for the tang:
1. if it goes from swimming normally to being skittish or hiding all of the time
2. if it stops eating
3. if it shows more aggression than usual (watch the fins on the other fish in the tank)
4. and the biggest sign... if it gets sick (if you have a healthy tang develop ich for no reason then the tank is usually getting too small and stressing it out).
So you get to choose just be prepared to deal with it if it does begin to feel cramped. the good thing is with the footprint your tank has you can get a much larger tank and keep your stand and hood the way they are.
good luck