How can I stop an angry cat from being aggressive to me?

It takes time and patience in order to build the cat's trust in you. Most angry cats are actually fearful and they attack because they feel unsafe. With this in mind make sure the cat always has an escape route out of the room, and you don't stand between him and the door. Also, avoid staring at the cat as this is a challenge to a fight in cat language. Instead, don't look at him directly and speak to him softly when in the same place. Talk to him when you put his food down, step back, and croon to him while he eats. Also, carry tasty cat treats in your pocket and drop them around you when he's about, to help him associate you with good things.