There are some rules of engagement to be considered here. On safety stuff, you do as you are told and inform, ask, tell, order passegers as appropriate. These are non-negotiable items. The only justification required is "Because you are required to do so". Do not add legal reasons or 'for insurance" or other such guff.
If you are trapped in the middle of a service that is time critical you will not have time to speak with Mr/Mrs Angry. Tell them your name, ask them theirs and tell them that you will come back to them either shortly, when you have finished the service or whatever. And do so. Address them by name, tell them that you have some time for them, pin back your ears and listen. Use firecat's flow.
You may be able to help, you may not. But unless you know what their problem is you will never know. Someone above mentioned that you should remember the attack is not personal, unless of course you did do something. In which case you can tell them you are sorry and didn't mean to upset them. You will also not be able to solve every problem. That's life. My last run in with a passenger was when he told me he would never fly with us again. "I've been stuck at your bloody airport for 18 hours and you've done nothing to help me. I hated every minute of this flight, the service was vile... etc." This was all shouted at me in my face. He was a lost cause and was foul to every member of the crew he met. He wanted a fight. "Excellent!" was my reply. "There's some really good airlines who will love your business. Good bye". I then 'guided' him off the aircraft but he was so keen to have a go he wasn't looking where he was going and tripped A over T. Shame!
But this guy was an exception. Most people will calm down when you listen. More will calm down after an explanation. Others will be satisfied when you solve their problem by you or others taking the appropriate action. A remainder will not be satisfied because there is nothing that can be done, but at least they know and you listened.
I hope this helps.
PM