What are angels? The Bible gives a few scriptural references to angels. In Hebrews 1:13-14 the Bible says "But to which of the angels said he at any time, Sit on my right hand, until I make thine enemies thy footstool? Are they not all ministering spirits, sent forth to minister for them who shall be heirs of salvation?" So here is a biblical definition of what angels are. The term angel or angels come from the Greek word (According to Strong"s Greek -Hebrew dictionary), "aggelos" (pronounced) ang'-el-os). "From ἀγγέλλω aggellō (probably derived from G71; compare G34; to bring tidings); a messenger; especially an “angel”; by implication a pastor: - angel, messenger." So although the biblical definition found in Hebrews 1:13-14 says God has made His angels to be ministering spirits, the Greek definition says they are also, "...by implication a pastor."
In a book I read it was mentioned of a woman's child who was sick. The mother put her long uncut hair over her child and God healed the child. I have also read in the same book the concept of the long uncut hair of a Christian lady taking the place of the covering cherub spoken of in Ezekiel 28:13-19. I don't believe there is any connection with the Apostle Paul's teaching in 1st Corinthians 11:2-16. If God in His mercy heals a sick child when a woman puts her long hair over the child, He does so not because of her long uncut hair but because of her faith and because of His mercy. Nowhere in the Bible is there any connection of special power given to the Christian woman because of her long uncut hair.
There is however much in the Bible concerning faith. In fact that is what the apostle Paul taught everywhere as mentioned in Acts 20:21. He said, "Testifying both to the Jews, and also to the Greeks, repentance toward God, and faith toward our Lord Jesus Christ." Let me get back to the subject of this posting. I believe what the writer of the Book of Hebrews was making reference to was angels that are spiritual beings. But the Greek meaning of the word, as stated before, can be pastors also. In the Book of Revelation in chapters 2 & 3 the Lord speaks to the angels ("aggelos" see above), by the Spirit, God's message to the churches, (see Adam Clarkes notes on Revelation some good and some not so good. I think it is commonly held that these were men who had rule over the churches. It becomes evident then that the word "angels" can mean more than spiritual beings.
This then provides a little more understanding to 1st Corinthians 11:10 where the Bible says, "For this cause ought the woman to have power on her head because of the angels." The word here for angels is again, "aggelos." It would then make more sense if taken into the context of what Paul was saying, eg, the woman being subject to the authority of the man. (see 1st Corinthians 11:3) This is a subject that has been discussed ad infinitum. In essence then the word angels can mean spiritual beings or ministers of the gospel.