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This is an interesting question. First, there was Gabriel who is named the angel who visited Zechariah to tell him the news of his wife Elizabeth’s miraculous pregnancy (Luke 1:13-19).
Later, God sent the angel Gabriel to visit Mary, a young Jewish virgin soon to be wed to Joseph (Luke 1:26-32). Gabriel told Mary that she was highly favored and would give birth to a son whom she was to name Jesus. He would be the long-awaited Son of the Most High.
An angel appeared to Joseph in a dream to tell him the news of Mary’s virgin birth (Matthew 1:20). In the birth narrative of Jesus, it states that heavenly hosts joined the angels who visited the shepherds keeping watch (Luke 2:13). Specifically, these heavenly hosts worshiped and praised God when they came to the shepherds declaring, “Glory to God in the highest heaven, and on earth peace to those on whom his favor rests” (Luke 2:14).
God sent his angels to the shepherds to share the good news of Jesus’ birth (Luke 2:9). The angels appearing to the shepherds was an indication of Jesus’ humble birth. He was born in a meager stable beside animals, he was laid in a manger, and the good news of his birth was told first to shepherds. Humble circumstances surrounded Jesus’ birth, which was fitting for the Son of the Most High who would lead a ministry that was marked by sacrificial love, servanthood, and surrendering to the Father’s will.
So, you tell me, why are angels important in the Christmas story?