The Angel of the Lord is the pre-incarnate appearance of Jesus. Old Testament appearances of Jesus are called 'Christophanies'. As the Angel of the Lord He appeared 10 times in the Old Testament.
1. He wrestled with Jacob - Gen. 32:24-30
2. He appeared to Jacob and redeemed him from all evil - Gen. 48:16
3. He appeared to Moss in the burning bush - Exod. 3:2
4. At the red sea He protected israel - Exod. 14:19
5. He guided and prepared Israel for the promised land - Exod. 23:20-23; Isa. 63:9;
6. He gave assurance to Joshua - Josh. 5:13-15
7. He appeared to Gideon - Judg. 6:11-12
8. He helped Elijah - 1 Kings 19:7
9. He saved Jerusalem from the Assyrian army - Isa. 37:36
10. He protected Daniels three friends in the furnace - Dan. 3:25
The Angel of the Lord Fulfills the same role as Christ: The Bible says "no one has seen God at any time," But Christ, who is God the second person of the trinity, has revealed exactly what God is like. If we want to know more about God then we look to Jesus. The Angel of the Lord fulfills the same roll as mediator between man and God, both in the Old Testament and the New. After Jesus incarnation, the angel of the Lord is no longer mentioned.
The Angel of the Lord Identifies Himself as God: The Angel of the Lord is also called names which God reserves for Himself alone. When the Angel of the Lord appeared in the burning bush (Ex 3:2), He is called "the LORD (Yahweh)" (Exodus 3:8). The Angel of the Lord also appeared to Abraham who called Him "Lord (Yahweh)" (Genesis 18:1). In Genesis 18 there were three angels who visited Abraham but when the other two left to go to Sodom, Abraham was left standing next to the "LORD" (Genesis 18:22). Similarly the Angel of the Lord identifies Himself as "wonderful" to Manoah's wife (Judges 13:18) - Jesus is the "wonderful counselor" (Isaiah 9:6). The angel of the Lord also answered Manoah's wife prayer which she had "prayed to the LORD." (Judges 13:8) He also received worship which no angel (apart from Satan) would do. John was rebuked by an Angel when he fell at it's feet in worship, the angel told John to only "worship God." Jesus received worship and so did the angel of the Lord.(Joshua 5:14-15)
The Angel of the Lord is a different person than the LORD: Even though the Angel of the Lord is identified as LORD (Yahweh), He is a different person than the LORD. In Zecharia 1:12-13 He speaks to the "Lord Almighty." This is an example of the Son speaking to the Father, just like in Psalm 110:1, or the Father speaking to the Son in Psalm 45:6 (CF Hebrews 1:8) Therefore in light of the three points above, the Angel of the Lord has to be Christ.