How do you handle an angry customer?
I stay calm and let them finish. Interrupting escalates; listening de-escalates.
First I acknowledge the emotion and the impact: "I understand this has cost you time, and I would be frustrated too." Then I apologise for the problem without over apologising or accepting blame on behalf of people I cannot speak for.
Next I move to facts. I restate the issue in my own words to confirm I have understood, and I ask for any details I need. Then I set expectations: what I can do, how long it will take and when I will next update them. I never promise something I cannot deliver.
If it is outside my authority I explain the escalation path rather than leaving them without an owner. Afterwards I follow up to confirm resolution. Most angry customers become loyal when they see you take ownership and communicate clearly.