Gabriel seems to be the same person who visited Daniel to explain the meaning of his visions. Since those visions were very troubling, Gabriel's message was welcome and an answer to prayer.
Gabriel also visited Zechariah as he served at the altar of incense in the Temple. In that case, Gabriel was there to explain how and why Zechariah's wife, Elizabeth, would conceive. Since the couple was old and childless, the message was certainly good news. Zechariah's response seems very similar to Abraham's and Sarah's:
Then Abraham fell on his face and laughed and said to himself, “Shall a child be born to a man who is a hundred years old? Shall Sarah, who is ninety years old, bear a child?”—Genesis 17:17 (ESV)
So Sarah laughed to herself, saying, “After I am worn out, and my lord is old, shall I have pleasure?”—Genesis 18:12 (ESV)
To a reader with any familiarity of Genesis, the theme of God providing a child to a childless couple would be an obvious connection. To a priest with familiarity of the Tanakh, a number of additional stories of God providing children should have come to mind. So Gabriel seems pretty justified in making Zechariah temporarily dumb "because you did not believe my words".
Now the coming of an angel must have been confounding to her and the message itself would not have been as welcome to an unmarried, betrothed, possibly teenage girl as it would have been to Elizabeth:
And the angel said to her, “Do not be afraid, Mary, for you have found favor with God. And behold, you will conceive in your womb and bear a son, and you shall call his name Jesus. He will be great and will be called the Son of the Most High. And the Lord God will give to him 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.”—Luke 1:30-33 (ESV)
I've emphasized the verbs, which indicate that a whole series of events will begin with her conceiving a son and ending with the Kingdom Gabriel had foretold to Daniel. It's not phrased as an offer, but as a certainty. That's quite a bit to absorb and so her question is natural and (perhaps a bit surprisingly) gets right to the crux of the problem:
And Mary said to the angel, “How will this be, since I am a virgin?”—Luke 1:34 (ESV)
She isn't so much questioning if the prophesy will come about, as she is questioning what the first step will be. She's asking the "Now what happens?" question. Now she might have recalled Isaiah 7:14 and understood it as a prophesy of a virgin conceiving, but that seems unlikely. Unlike the mairead of examples of barren women providing their aging husbands with children, the Tanakh doesn't offer many cases of unmarried women giving birth. The cultural normative was to remain a virgin until marriage. So her question was likely intended to get direction about how to proceed with her engagement.
Perhaps more to the point, Luke's Greek and Roman readers, would likely have connected the story to the many myths about Zeus seducing or raping mortal women. Mark avoided the issue by starting the story with Jesus as an adult, John takes a highly philosophical approach that also avoids details of the nativity, and Matthew focuses on Joseph's response to the news rather than Mary's. So Luke was the only early account that took on the difficulty of the virgin birth head on.
His solution is to describe the moment of Mary's conception as a creation event:
And the angel answered her, “The Holy Spirit will come upon you, and the power of the Most High will overshadow you; therefore the child to be born will be called holy—the Son of God. And behold, your relative Elizabeth in her old age has also conceived a son, and this is the sixth month with her who was called barren. For nothing will be impossible with God.”—Luke 1:35-37 (ESV)
The callback would be to the first chapter of Genesis:
The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God was hovering over the face of the waters.—Genesis 1:2 (ESV)
Mary remains a virgin because the Spirit of God creates the child ex nihilo. He will "be called holy—the Son of God", not because His mother is untainted by sex, but because God caused Him to be created in a unique way and without violating Mary. Notice that the definite tone continues: these events will happen. But Mary takes the opportunity to give her assent to the arraignment:
And Mary said, “Behold, I am the servant of the Lord; let it be to me according to your word.” And the angel departed from her.—Luke 1:38 (ESV)
Gabriel didn't ask, but Mary behaves as if he had given her an option. Again, this diffuses the possibility of a rape scenario. Luke further emphasizes Mary's willingness to go along with the plan and her acknowledgment of God's blessing to her in the rest of the chapter (especially The Magnificat). It's also helpful to contrast Zechariah's unbelief with Mary in order to highlight her faithful response.
Zechariah responses to welcome, good news with unbelief. Mary responds to troubling news with first with practicality and faithfulness in the end.