People that are/react angry are afraid of something.
Fighting and fleeing are responses to fear.
If you encounter a person who is (or becomes throughout a conversation) angry; what you definitely shouldn’t do is reinforce their anger by demanding their attention or even worse, demand their understanding of your point of view.
Your brain is built so that this would only shut off the angry person more. They now must have your understanding first, and your compliance second. It’s not giving in, it’s your tactical approach to anger.
Angry people are in fear of something.
And probably that something is future-projected (severe) physical or emotional discomfort. From something or someone else (or worse, more somethings or someones).
And, probably, they don’t even know they’re fearful, let alone what they fear.
Empathy is the solution.
Your task is to discover the discomfort. Like finding a missing piece of a puzzle.
Where’s the pain? What’s the pain? Who creates the pain?
Because that pain is your common opponent. And you – together with the angry person – are fighting that opponent. But you don’t know who the opponent is. So first, you’ll need to figure that out.
If you discover the pain, speaking that pain works like a relief. It will relieve a lot of tension, when the other person feels understood.
Once you know what or who the opponent is, you’ll easily figure out a solution together. Because it will most certainly will be easy for you to meet the need.
Probably it’s easy to meet the need. Or even better, being understood and heard was the only need and it’s already met by speaking about it.
Anger (or any emotion) is contagious. Don’t fall for the trap of being infected. Take a step back. Be compassionate. Fighting their fear together is the right way.