Who was "the Angel of the LORD"? "Angel" of course, means MESSENGER.
I believe He was - and IS - the Son of God. The Angel of the LORD existed long before Jesus the man, was born in Bethlehem.
Genesis 22:1-18 “But the Angel of the LORD [Yehovah] called to him from heaven and said, ‘Abraham, Abraham!’ And he said, ‘Here I am.’ And He said, ‘Do not lay your hand on the lad, or do anything to him; for now I know that you fear God, since you have not withheld your son your only son, from Me.’”
NOTE: The Angel of the LORD speaks as Yehovah, saying, “You have not withheld your son . . . from Me.”
Genesis 31:10-13 Jacob said, “The Angel of God spoke to me in a dream saying, ‘I am the God of Bethel, where you anointed the pillar and where you made a vow to Me.’”
Exodus 3:2-6 “And the Angel of the LORD [Yehovah] appeared unto him in a flame of fire out of the midst of the burning bush:”(v.4). “God [‘elohiym] called to him out of the midst of the bush,”(v.5). “Take your sandals off your feet, for the place where you stand is holy ground.”(v.6). “I am the God [‘elohiym] of your father--the God [‘elohiym] of Abraham, the God [‘elohiym] of Isaac, and the God [‘elohiym] of Jacob.”
Exodus 3:13-14 [From the burning bush] “And God [‘elohiym] said to Moses, ‘I AM WHO I AM,’
NOTE: The Angel (the messenger) OF the LORD, speaks AS God. A created angel, would say "Thus says the LORD . . . .". but this Angel speaks AS GOD.
Exodus 23:20-21 “And God [‘elohiym] spoke all these words, saying . . .” (Exo 20:1). “Behold, I send an Angel before you to keep you in the way and to bring you into the place 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.”
NOTE: To an ancient Israelite - to Moses, the phrase “My name is in Him” meant, “He is My Son.”
The Angel OF the LORD was NOT God the Father, yet he spoke as God.
When the Son acted as the agent of His Father, He took His Father’s name. The same applied, when He acted on behalf of the Father as “the Angel of the LORD” during the period called the Old Testament.
Judges 2:1-2 “And the Angel of the Lord came up from Gilgal to Bochim, and said, I made you to go up out of Egypt, and have brought you unto the land which I swore unto Your fathers, and I said, I will never break My covenant with you.” “. . . but you have not obeyed My voice” (v.2).
May I refer you to a study I did on this subject. http://www.prophecyviewpoint.com/htdocs/11-The Mediator.pdf
If your browser does not take you to the pdf, then just go to prophecyviewpoint.com, and look under the button "Dominion Lost". You will see another button for "The Mediator".