After years of seeing jocks handle it both ways, ignore or deplore, I think the best way is to answer it with comedy. Why? Because I remember seeing Stephen Capen get a really hateful phone call. He had the caller on a speakerphone in the studio and the guy went on a rant, telling Capen what a jerk, etc. he was. Capen proceeded to answer with an angry, "oh YEAH? You think I'm a JERK? Well....you're RIGHT!" At which point, the listener totally cracked up. By the end of the call, the listener was a total fan because Capen just made him laugh.
SO, I think the best way is...make them laugh. Not worth it to make enemies, not in this biz. We are on the air to entertain. Many people don't know you and don't care, they are just pissed off people with no lives, so...they are just looking for someone/ANYONE to pick on and to pick a fight. But don't go to their level. Be above it. You should not take the attack personally. if not you, then they'd target someone else on the radio, right?
It's a real challenge to figure out ways to make pissed off angry listeners laugh, but trust me, if I can do it, so can you!