I used to live in Angel and you have 2 options.
You can go to Stansted from Liverpool St Station which is about a 10-15 cab from Emirates and the train is 46 mins. Return train is £28 i think.
Or
Fly from London City with BA, you can get a DLR train on the Northern Line straight to the airport and takes about 15-20 mins from Angel. Means you can get on the tube at Emirates instead of having to get a cab and hoping the traffic is not too bad!!