Watch your reactions closely in situations where you are annoyed or angry. These are good times to practice mindfulness and realise that mindfulness has nothing to do with forcibly getting rid of these feelings. It's about sitting with these feelings, observing them and letting them marinate.
Remind yourself that you don't have to act on these feelings straight away, and that you can allow yourself more time to process them by just observing these feelings, through the lens of mindfulness. This way, you can teach yourself to be more patient, rather than projecting these feelings out into the world, or trying to force the world into the state you would like it to be.
Adapted from: Wherever You Go, There You Are by Jon Kabat-Zinn