Make a map with an 80 armor gt, some peons and a computer with a cat. Set up the peons, gt and the enemy cat in a way that the cat attacks the tower from various angles. Try to rep the tower and take notes ;p
Of course for example if you rep the tower with your peon closing in an orthogonal angle to the angle of the cat's line of fire, you won't take damage. You can also micro 2 peons, periodically repairing and moving 1 tile away from the gt.
I noticed that in more 'direct' angles, the peon sometimes takes damage and sometimes does not. I don't really get it either.