Empathize with the angry customer
Empathizing doesn't take much effort on your part, and it has a powerful impact on a tense situation involving an angry or difficult client. When you empathize with the customer by letting him or her know that you understand how he or she feels, you release much of the tension out of the situation.
Source: Sales trainer/author Dave Kahle
Picture a balloon that you have blown up almost to the point of bursting. There is tremendous tension inside the balloon pushing outward. But when you open the bottom, and let some of that pressure out, the balloon relaxes. Same thing when you empathize with the customer. Picture yourself letting air out of the bottom of that balloon.