11 But let us travel once more in our journey of instruction over the lessons taught in the holy Law of God. The Angel of God speaks to Hagar; and this same Angel is God. But perhaps His being the Angel of God means that He is not true God. For this title seems to indicate a lower nature; where the name points to a difference in kind, it is thought that true equality must be absent. The last book has already exposed the hollowness of this objection; the title of Angel informs us of His office, not of His nature.
I have prophetic evidence for this explanation; Who makes His angels spirits, and His ministers a flaming fire. That flaming fire is His ministers; that spirit which comes, His angels. These figures show the nature and the power of His messengers, or angels, and of His ministers. This spirit is an angel, that flaming fire a minister, of God. Their nature adapts them for the function of messenger or minister. Thus the Law, or rather God through the Law, wishing to indicate God the Son as a Person, yet as bearing the same name with the Father, calls Him the Angel, that is, the Messenger, of God.
The title Messenger proves that He has an office of His own; that His nature is truly Divine is proved when He is called God. But this sequence, first Angel, then God, is in the order of revelation, not in Himself. For we confess Them Father and Son in the strictest sense, in such equality that the Only-begotten Son, by virtue of His birth, possesses true Divinity from the Unbegotten Father. This revelation of Them as Sender and as Sent is but another expression for Father and Son; not contradicting the true Divine nature of the Son, nor cancelling His possession of the Godhead as His birthright.
For none can doubt that the Son by His birth partakes congenitally of the nature of His Author, in such wise that from the One there comes into being an indivisible Unity, because One is from One.
Source: On the Trinity (New Advent)