In Genesis 16:8 - 9 an angel of the Lord comforts Hagar who, although pregnant with her son Ishmael, is running away from Sarah and Abraham. The spirit-based individual in human form promises her that she will have many children, grandchildren, and so on and even foretells some of Ishmael's traits (verses 10 - 12). The Bible indicates this special angel was likely divine.
What evidence exists that the angel of the Lord in the Old Testament was Jesus Christ? He is not only able to make prophetic announcements but also to cause events to happen at a particular time and place (Genesis 16:10 - 12).
Hagar, after talking with an "angel" stated, ". . . You are a God of Seeing! For she said, 'Even here have I seen Him that sees me?'" (Genesis 16:13, HBFV). Hagar did not believe she was talking to an angel but rather directly with the Lord God!
The angel of the Lord later appears to Abraham just before he is to sacrifice his only son Isaac (Genesis 22:11). Because Abraham passed the extreme test of faith given him, he is informed several blessings will come his way.
Genesis 22:16 is especially noteworthy, and lends itself to the belief that Jesus was interacting directly with Abraham, when the "angel" states, "'By Myself have I sworn,' says the Lord, 'because you have done this thing . . . that in blessing I will bless you . . .'" (verse 16).
Jacob, the son of Isaac, also had encounters with this unique spiritual being. In a dream (Genesis 31) an individual referred to as the "angel of God" states he is the One Jacob worshipped in Bethel (verse 11, 13). The connection between these two references is undeniable, and points to Jacob directly interacting with a member of the Godhead as only God can rightfully receive worship.
Later, Jacob wrestles all night with a "man" who refuses to disclose his name but grants his request for a blessing (Genesis 32). He also gives Jacob the new name "Israel." The patriarch is convinced he has wrestled not with a angel but with the Lord God who took on the form of a man! The prophet Hosea later seems to confirm this observation (Hosea 12:3 - 4).
Moses is called to serve when he sees a flame that does not consume a bush (see Exodus 3). A voice calls to him and proclaims that He is the God of his fathers Abraham, Isaac, and Jacob (verse 6). Clearly, the voice in the bush is speaking as a divine Being.
In verse 14 of Exodus 3 it is revealed "I AM" is his name. This designation of 'I AM' is the same one the Lord Jesus Christ will apply to himself (John 8:58 - 59).
At mount Sinai the Israelites are told that an Angel will accompany them on their way to the land promised them (Exodus 23). This being not only has God's Name upon him but also has the authority to command the Israelites obey him. He also has the authority to forgive the breaking of the law (verse 21), all of which suggests he is divine.
God, after Israel sins in the golden calf incident, decides to have an angel go with them (Exodus 33:2 - 3). Due to a intense intercession by Moses, he agrees to keep his initial promise of leading the children of Israel into the Promised Land (Exodus 33:15 - 17).
The Apostle Paul would later state that "the spiritual rock" that went with Israel was none other than the Lord Jesus Christ (1Corinthians 10:4).
Why would God choose to reveal Himself to man as the angel of the Lord? These appearances of Jesus, before his human birth, show He is a personal Being who loves and cares about those he has created.
These appearances are part of God the Father's advance proclamation of the coming of his son as the Messiah. For further study on the fascinating subject of the Angel of the Lord and his true identity, please see the book "Christ in the Old Testament" by James Borland.