Then you walk alongside this wall, until you reach the next corner of the building. And - guess what! - turn to face along the third wall. You've then just turned through the second exterior angle of the polygon.
... and so on, until you come back to your starting point. What can you say about the sum of the angles that you've turned through?
Now I realise this isn't a conventional geometry proof, but you can perhaps see how to turn it into one. Have a go!