Deal with angry people by matching their emotions

Whenever you are discussing emotionally charged matters or need facts about them, let the speaker finish before you jump in. Count to ten if you must.
It will seem like an eternity, but letting the flustered fellow finish is the only way they’ll hear you when it’s your turn.

Let them emote.
Hear their facts but empathize like mad with their emotions.

Now when their emotional storm is calmed, deal with them by apologizing properly and giving them a token of apology if possible.