It is for this reason that a woman ought to have authority over her own head, because of the angels. (NIV)
Therefore she should [be subject to his authority and should] have a covering on her head [as a token, a symbol, of her submission to authority, that she may show reverence as do] the angels [and not displease them]. (AMP)
For this cause ought the woman to have power on her head because of the angels. (KJV)