Use this:
=IF(A3<=180,1,IF(A3<=190,2,IF(A3<=200,3,IF(A3<=210,4,IF(A3<=220,5,IF(A3<=235,6,"ABE"))))))
By the way, I modified it to include if it's 180 then it's a 1, because you skip that possibility.
less than 180 and greater than or equal to 181 misses out on 180
if(a3<180, 1),
if(a3>=181, a3<=190,2),