The angel Gabriel appeared to John the Baptists father before Jesus" mother. There is a significant difference in their reactions as it pertains to faith. I think the way Luke is arranged is meant to contrast the two events. since the same angel appears to both any difference in their responses is a reflection of disposition in relation to the angel and since Gabriel is Holy their disposition towards God.
Luke 1
. 11 Then there appeared to him an angel of the Lord, standing at the right side of the altar of incense. 12 When Zechariah saw him, he was terrified; and fear overwhelmed him. 13 But the angel said to him, “Do not be afraid, Zechariah, for your prayer has been heard. Your wife Elizabeth will bear you a son, and you will name him John. 14 You will have joy and gladness, and many will rejoice at his birth, 15 for he will be great in the sight of the Lord. He must never drink wine or strong drink; even before his birth he will be filled with the Holy Spirit. 16 He will turn many of the people of Israel to the Lord their God. 17 With the spirit and power of Elijah he will go before him, to turn the hearts of parents to their children, and the disobedient to the wisdom of the righteous, to make ready a people prepared for the Lord.” 18 Zechariah said to the angel, “How will I know that this is so? For I am an old man, and my wife is getting on in years.” 19 The angel replied, “I am Gabriel. I stand in the presence of God, and I have been sent to speak to you and to bring you this good news. 20 But now, because you did not believe my words, which will be fulfilled in their time, you will become mute, unable to speak, until the day these things occur.”
Zecharia: "111 Then there appeared to him an angel of the Lord, standing at the right side of the altar of incense. 1 2 When Zechariah saw him, he was terrified; and fear overwhelmed him
Mary:"And he came to her and said, “Greetings, favored one! The Lord is with you.”[b] 29 But she was much perplexed by his words and pondered what sort of greeting this might be.
This contrasts the dispositions of a holy and aged Priest of Israel with a teenage girl of Israel.
The beginning of faith in Jesus for Mary believed what the angel said. Zecharia didn't.
Luke 1
. 11 Then there appeared to him an angel of the Lord, standing at the right side of the altar of incense. 12 When Zechariah saw him, he was terrified; and fear overwhelmed him. 13 But the angel said to him, “Do not be afraid, Zechariah, for your prayer has been heard. Your wife Elizabeth will bear you a son, and you will name him John. 14 You will have joy and gladness, and many will rejoice at his birth, 15 for he will be great in the sight of the Lord. He must never drink wine or strong drink; even before his birth he will be filled with the Holy Spirit. 16 He will turn many of the people of Israel to the Lord their God. 17 With the spirit and power of Elijah he will go before him, to turn the hearts of parents to their children, and the disobedient to the wisdom of the righteous, to make ready a people prepared for the Lord.” 18 Zechariah said to the angel, “How will I know that this is so? For I am an old man, and my wife is getting on in years.” 19 The angel replied, “I am Gabriel. I stand in the presence of God, and I have been sent to speak to you and to bring you this good news. 20 But now, because you did not believe my words, which will be fulfilled in their time, you will become mute, unable to speak, until the day these things occur.”
Zecharia: "111 Then there appeared to him an angel of the Lord, standing at the right side of the altar of incense. 1 2 When Zechariah saw him, he was terrified; and fear overwhelmed him
Mary:"And he came to her and said, “Greetings, favored one! The Lord is with you.”[b] 29 But she was much perplexed by his words and pondered what sort of greeting this might be.
This contrasts the dispositions of a holy and aged Priest of Israel with a teenage girl of Israel.
The beginning of faith in Jesus for Mary believed what the angel said. Zecharia didn't.