Psalm 80 shows that the Shepherd of Israel sat between the Cherubim in the Holy of Holies, showing that Jesus Christ is the God who interacted with Israel.
The identical actions of the Lord and the Angel of the Lord show they are the same Being. The God known by Abraham, Isaac, Jacob, and Moses was Jesus Christ.
Among God's many attributes are those that He cannot pass on to others because they define Him. God's attribute of omnipotence defines His power over all.