You being angry makes somebody else angry and their being angry makes you angry. Don't continue in your anger. When we are angry, we do things that we are going to eventually regret.
It is important for you to have a fountain of peace, a place where peace flows abundantly. If you are doing practices that help eliminate anger and create peace in your life before you even enter into a situation that might cause you to be angry then you are already one step ahead of it.

Being angry is being on fire so stop, drop, and roll.

You stop the conversation, drop the reason why you need to stop talking, and leave the space leaving the conversation and the person if possible for a temporary time.
Then you identify the root of your anger. The person who has done something that angered you is not the sum of that action.
You address the cause of your anger. You go back to the person that angered you and tell them what you have learned from reflecting on your anger.