Power on her head (ἐξουσίαν)

Not in the primary sense of liberty or permission, but authority. Used here of the symbol of power, i.e., the covering upon the head as a sign of her husband's authority. So Rev., a sign of authority.

Because of the angels

The holy angels, who were supposed by both the Jewish and the early Christian Church to be present in worshipping assemblies. More, however, seems to be meant than "to avoid exciting disapproval among them." The key-note of Paul's thought is subordination according to the original divine order. Woman best asserts her spiritual equality before God, not by unsexing herself, but by recognizing her true position and fulfilling its claims, even as do the angels, who are ministering as well as worshipping spirits (Hebrews 1:4). She is to fall in obediently with that divine economy of which she forms a part with the angels, and not to break the divine harmony, which especially asserts itself in worship, where the angelic ministers mingle with the earthly worshippers; nor to ignore the example of the holy ones who keep their first estate, and serve in the heavenly sanctuary.

1 Corinthians 11:10 Parallel Commentaries

power. That is, a covering in sign that she is under the power of her husband. [Exousia,] appears here to be used for the sign or token of being under power or authority, that is, a veil, as Theophylact, (Ecumenius, and Photius) explain; and so one MS. of the Vulgate, the Sixtine edition, and some copies of the Itala, have velamen.

Genesis 20:16 And to Sarah he said, Behold, I have given your brother a thousand pieces of silver: behold, he is to you a covering of the eyes...

Genesis 24:64,65 And Rebekah lifted up her eyes, and when she saw Isaac, she lighted off the camel...

because.

Ecclesiastes 5:6 Suffer not your mouth to cause your flesh to sin; neither say you before the angel, that it was an error...

Matthew 18:10 Take heed that you despise not one of these little ones; for I say to you...

Hebrews 1:14 Are they not all ministering spirits, sent forth to minister for them who shall be heirs of salvation?