The actual head coverings that Paul was speaking about were these:
1. A wife's spiritual head covering - her husband
2. A wife's natural head covering - her hair
Paul's point was that if it isn't shameful for a wife to disregard her spiritual head covering or to usurp authority over her husband, then let her also shave her head or remove her natural head covering. In regard to the God-given authority (which is not synonymous with abuse or domination, btw) of a husband in relation to his own wife, Paul later said in this same epistle:
"Let your women keep silence in the churches: for it is not permitted unto them to speak; but they are commanded to be under obedience, as also saith the law. And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church. What? came the word of God out from you? or came it unto you only? If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord. But if any man be ignorant, let him be ignorant. Wherefore, brethren, covet to prophesy, and forbid not to speak with tongues. Let all things be done decently and in order." (I Corinthians 14:34-40)
Contextually, "your women" were "your wives" who were instructed to "ask their husbands at home" and this is part of the "all things" that Paul was instructing the Corinthians to "do decently and in order". Going back to "the angels" for a moment, it seems as if they are watching over things to see whether or not they truly are "done decently and in order" and I believe that this is what Paul was talking about in the text from chapter 11. IOW, a wife ought to have her husband as her spiritual covering because that is the "order" that God created for marriage where the husband is representative of Christ and the wife is representative of His church even as Paul explained in Ephesians chapter 5.