1 Corinthians 11:5-7

11:5 But any woman who prays or prophesies with her head uncovered disgraces her head, for it is one and the same thing as having a shaved head. 11:6 For if a woman will not cover her head, she should cut off her hair. But if it is disgraceful for a woman to have her hair cut off or her head shaved, she should cover her head. 11:7 For a man should not have his head covered, since he is the image and glory of God. But the woman is the glory of the man.

1 Corinthians 11:10

11:10 For this reason a woman should have a symbol of authority ¹  on her head, because of the angels. ² 

1 Corinthians 11:13

11:13 Judge for yourselves: Is it proper for a woman to pray to God with her head uncovered?

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¹ sn Paul does not use a word specifying what type of “covering” is meant (veil, hat, etc.). The Greek word he uses here (ἐξουσία exousia; translated symbol of authority) could be (1) a figure of speech that may substitute the result (the right to participate in worship) for the appropriate appearance that makes it possible (the covered head). Or (2) it refers to the outward symbol (having the head covered) as representing the inward attitude the woman is to possess (deference to male leadership in the church).

² sn Paul does not explain this reference to the angels, and its point is not entirely clear. It seems to reflect an awareness that angels are witnesses to church life (cf. Eph 3:10) and would be particularly sensitive to resistance against God’s created order.