balrogs and wings debate

Okay, I was reading an old thread that was a long debate about wether or not Balrogs have wings. I just finished reading Fellowship for about the millionth time, and I noticed this passage because I was wondering why everyone depicts Balrogs with wings, because I didn't think they had them. This is what it says about the Balrog:

"The Balrog made no answer.The fire in it seemed to die, but the darkness grew. It stepped forward slowly on to the bridge, and suddenly it drew itself up to a great height, and its wings were spread from wall to wall..."

Tolkien gave them wings, therefor they are winged. I think this is conclusive evidence, but am open to more debate.