Do angels have wings?

Everyone knows that angels have wings.  Every picture we see of angels shows them with wings.  However there is one problem.  Some of the things said about angels in the Bible seem to contradict this belief.

Before God destroyed Sodom he sent two angels to take Lot and his family out of the city.

The two angels came to Sodom in the evening, and Lot was sitting in the gate of Sodom. When Lot saw them, he rose to meet them and bowed himself with his face to the earth and said, “My lords, please turn aside to your servant’s house and spend the night and wash your feet. Then you may rise up early and go on your way.”

They said, “No; we will spend the night in the town square.”  But he pressed them strongly; so they turned aside to him and entered his house. And he made them a feast and baked unleavened bread, and they ate.

But before they lay down, the men of the city, the men of Sodom, both young and old, all the people to the last man, surrounded the house.  And they called to Lot, “Where are the men who came to you tonight? Bring them out to us, that we may know them.”

Genesis 19:1-5

The men of Sodom thought the angels were men and tried to attack them.  Don’t you think that if they had wings the men would have known they would have realized there was something different about them and they wouldn’t have been so anxious to harm them?

The four living creatures

Revelation chapter 4 describes John’s being carried in the spirit up to Heaven, into the throne room of God.  Among the sights he sees there are four living creatures that surround the throne.

And around the throne, on each side of the throne, are four living creatures, full of eyes in front and behind: the first living creature like a lion, the second living creature like an ox, the third living creature with the face of a man, and the fourth living creature like an eagle in flight. And the four living creatures, each of them with six wings, are full of eyes all around and within, and day and night they never cease to say,
“Holy, holy, holy, is the Lord God Almighty,
who was and is and is to come!”
Revelation 4:6-8

Many believe these creatures are cherubim because their description resembles that of of the cherubim that appeared to Ezekiel.

As for the likeness of their faces, each had a human face. The four had the face of a lion on the right side, the four had the face of an ox on the left side, and the four had the face of an eagle.
Ezekiel 1:10

Both descriptions include similarities to a man, a lion, an ox, and an eagle.  But there is one difference.  Each individual cherub resembled all four of these; each of the living creatures was like one of them.