Jacob's wives are told what he saw while he was dreaming. In his dream the 'angelic' being calls himself the God Jacob worshipped in Bethel. This is referencing a prior revealing dream (Genesis 28:10-15). These Bible verses suggest that Jacob viewed the being he saw in a dream as divine. He later would have a seemingly odd encounter with the same Being of his dream.
24 Afterwards, Jacob went back and spent the rest of the night alone. A man came and fought with Jacob until just before daybreak. 25 When the man saw that he could not win, he struck Jacob on the hip and threw it out of joint (Genesis 32)
Jacob wrestles all night with a "man" who refuses to disclose his name but grants Jacob's request for a blessing. He gives Jacob the new name Israel, and afterwards Jacob is convinced that he has wrestled with God. The prophet Hosea later writes of Jacob the following.
When Jacob grew up, he fought against God — 4 he fought against an angel and won. (Hosea 12:3-4).
These passages and others describe a messenger of God who is both distinct from him and divine.
Testing the faith of Abraham
When they came to the place which God had told him about, Abraham built an altar and arranged the wood on it. 11 But the angel of the Lord called to him from heaven . . . 12 'Don’t hurt the boy . . . (Genesis 22)
God tests Abraham's faith by asking him to sacrifice his only son Isaac. The angel of the Lord appears just before Isaac is to be killed. Because he passed this extreme test of his faith, Abraham is told he will be blessed in several ways (verses 16-18). Verse 12 of Genesis 22 strongly implies the divine nature of the Being who spoke to Abraham as well as verses 15 to 18.
Moses and the burning bush
There the angel of the Lord appeared to him as a flame coming from the middle of a bush. Moses saw that the bush was on fire but that it was not burning up. 5 God said, 'Do not come any closer. Take off your sandals, because you are standing on holy ground.' (Exodus 3)
Moses' eye is caught by a flame (verse 2) that does not consume a bush. 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 the same chapter it is revealed "I AM" is his name. This designation of 'I AM' is the same one Jesus Christ will apply to himself.
Leading the Israelites to the Promised Land
Behold, I send an Angel before you to keep you in the way and to bring you into the place which I have prepared. Beware of Him and obey His voice; do not provoke Him, for He will not pardon your transgressions; for My name is in Him . . . For My Angel will go before you . . . (Exodus 23)
At mount Sinai the Israelites are told by God He will send a spiritual being with them on their way to land He has promised them. This being not only has God's Name but the Israelites are told they must obey him. He also is able to forgive the breaking of God's law (verse 21), which suggests he is divine.
God, after Israel sins by making and worshipping a golden calf, decides to have an angel go with them (Exodus 33:2-3). Due to a strong intercession by Moses, he agrees to keep his initial promise. He will go with the children of Israel (Exodus 33:15-17). Paul the apostle would later state that "the spiritual rock" that went with ancient Israel was none other than the Lord Jesus Christ (1Corinthians 10:4).
All of this information begs one simple question: WHY would God choose to reveal Himself to man as the angel of the Lord? These appearances of Jesus before his birth shows that the Creator is a personal Being who loves and cares about those he has created. In the final analysis, these appearances were part of the Father's advance proclamation of the coming of his son as the Messiah.