Is There an Easy Way to Stop Feeling Angry or Annoyed?

YES THERE IS. Anger and annoyance come from the conclusions you've drawn about the meaning of an event. You conclude that you were insulted or disrespected, and then you feel anger in response to the disrespect.

For example, when someone does X, it means they think you're stupid. But what if that's not what it means? Then your anger would just be needless suffering, right?

Try this: Next time you feel angry or annoyed because someone did something, ask yourself what you think the action meant. Then ask yourself What else could it mean? Your first conclusion might not be the best one, so ask it a few times. Your anger will diminish as your certainty about the meaning of the event diminishes.

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Here's a conversational chapter on optimism from a future book:
Conversation on Optimism

If worry is a problem for you, or even if,you would like to simply worry less even though you don't worry that much, you might like to read this:
The Ocelot Blues

Learn how to prevent yourself from falling into the common traps we are all prone to because of the structure of the human brain:
Thoughtical Illusions

next: Immediate Relief