Promise of an eternal king (Promise given to David in 2 Samuel 7)
The angel tells Mary that "the Lord God will give [Jesus] the throne of His father David. And He will reign over the house of Jacob forever, and of His kingdom there will be no end."
Promise of an eternal priest (Promise given to David in Psalm 110; see also Hebrews 5-7)
The angel tells Joseph that Jesus "will save His people from their sins."
Promise of a great name and victory (Promise given to Abram in Genesis 12)
The angel tells Mary that Jesus "will be great", echoing the promise God gave to Abram that He will "make your name great".
The angel tells Joseph that Jesus "will save His people from their sins", echoing the promise that God gave to Abram saying that He will "bless those who bless you and I will curse him who curses you." The priest Zechariah describes the promise as deliverance "from the hand of our enemies."
Promise of the Son of God (Promise given to Ahaz in Isaiah 7, promise (riddle?) given to David in Psalm 110 - Matthew 22)
The angel tells Mary that Jesus "will be called the Son of the Highest ... the Son of God"
In writing about the angel's message, Matthew explains that this was done to fulfill the promise that Jesus would be called "God with us."