People become angry when they are lied to for a variety of reasons. For some it is the assumption of belief, as though the person being lied to is 'stupid enough to swallow a lie.'
For other people, the anger comes as a result of feeling taken advantage of, or having trust abused as a result of the lie. Anger is a combination of adrenaline responses, emotional reactions to things that relate to past hurts or unresolved issues, and the desire to do something about any or all of it.
The bottom line is, when a person is lied to, there are many factors at work; the trust of the 'victim' of the lie is violated, there are unknown hidden motivations of the liar, and the consequences of the lie. Sorting it all out will take time and a clear head. It's best to wait until your anger has passed before trying to deal with the person who has decieved you.
If you feel angry as a result of being lied to, know that it is a quite normal and healthy response. How you act on that anger determines the quality of resolution of the situation. If you can reason your way through your anger to a constructive solution you will be able to better deal with the issue and put it behind you. You may or may not be willing to sever a relationship with someone who lies to you; the important thing is to let them know it is simply not acceptable.