You're not angry, you're hurt.

One of my professors used to say "dodge the anger and get to the tears". We therapists sometimes describe anger as a "secondary emotion", one that comes about due to a primary emotion, usually pain or sometimes fear. You can on occasion have "pure" anger, like someone steals your parking spot, but those moments are fleeting and disappear almost as soon as they appear (and if they don't, we need to talk).

To have the kind of long-lasting and resentment-fueled anger that arises in relationships, it almost always is masking a hurt; a pain or disappointment that is difficult to address directly. The problem is the anger often leads to conflict, and hinders our ability to resolve the hurt and get what we really want.

For example, it is very easy to get angry that your partner forgot to get something important you need for a project. "You're so inconsiderate and self-centered" will lead to an argument, not a resolution. Defensiveness and traded accusations will easily manifest. But it is much easier than saying "it really hurts my feelings when you don't prioritize things that I need, it makes me feel unimportant and like I don't matter". That is something important to say, and truly the cause of your pain(and hence anger), but it makes us very vulnerable. However, this conversation will go very differently, and will create different reactions in both parties. It also can be resolved: apologies can be made, reassurances uttered, and pledges made to do better. 

All those things offer opportunity for healing and improvement, and not just another argument. 

So the next time you feel angry, pause a moment and think about WHY you're angry. Odds are you will in truth be hurt by something, and that pain is what needs to be discussed and resolved with the one who hurt you.