maybe your 'angry' side is your ego. everyone has one, and depending on how out of control you let it get.. the more power it has over you.
To quote this amazing book i just finished reading, "Recognize the ego for what it is: a collective dysfunction, the insanity of the human mind. Once you see the ego for what it is, it becomes much easier to remain nonreactive toward it. "
it also brings up a really interesting idea, that Thinking "happens" to you... those crazy thoughts that pop into your head aren't really you, it's your ego. It's a good book, i highly recommend it and it might help you, it helped me.
A New Earth by Eckhart Tolle