וַיֹּ֤אמֶר לָהּ֙ מַלְאַ֣ךְ יְהוָ֔ה הִנָּ֥ךְ הָרָ֖ה וְיֹלַ֣דְתְּ בֵּ֑ן וְקָרָ֤את שְׁמוֹ֙ יִשְׁמָעֵ֔אל כִּֽי־שָׁמַ֥ע יְהוָ֖ה אֶל־עָנְיֵֽךְ׃
און דער מלאך פֿון גאָט האָט צו איר געזאָגט: זע, דו ביסט טראָגעדיק, און געבערסט אַ זון, זאָלסטו רופֿן זײַן נאָמען יִשמָעֵאל, װײַל גאָט האָט צוגעהערט דײַן פּײַן.
Rashbam
The word is derived from the root תלה, “to hang,” We find it used in this sense in Genesis 40,22 in connection with Pharaoh hanging the chief of the bakers, as well as in Judges 5,12 where the word שביך בן אבינועם is derived from the root שבה, Similarly, the word עניך in Genesis 16,11 כי שמע ה' אל עניך, “for the Lord has paid heed to your suffering,” is derived from the root ענה.
Ramban
AND HIS KING SHALL BE HIGHER THAN AGAG. “Their first king [Saul] will conquer Agag208I Samuel 15:8. king of the Amalekites. Agag is here called by his name before he was born.209This whole paragraph — from “Agag is here called” until “…before they were born” — is not found in our texts of Rashi. Similar cases are [the expressions]: to Cyrus, whose right hand I have holden;210Isaiah 45:1. Behold, a son shall be born unto the house of David, Josiah by name.211I Kings 13:2. So also were the names of Isaac,212Genesis 17:19. Ishmael,213Ibid., 16:11. and Solomon214I Chronicles 22:9. [given before they were born]. AND HIS KINGDOM — that is, Jacob’s — SHALL BE EXALTED more and more, because David and his son Solomon will come after him [Saul].” This is Rashi’s language, and he has explained it well.
It is possible that every king of the Amalekite people was called Agag, because the first king whom they set up over them was so called [Agag], and thus all his descendants who occupied his throne were called by his name,215Thus there is no need to say, as Rashi did, that Agag here refers to the specific Amalekite king of King Saul’s days, and that his name is foretold a few hundred years before he was born, as Scripture would not foretell the birth of a wicked man. as are most kings even nowadays, who are called by the name of those who [originally] seized the kingdom. So also Haman the Agagite216Esther 3:1. [was so called] because he was a descendant of that royal family. For it is unlikely that the prophet [Balaam] would cite the name of a wicked man [Agag] even before he was formed in the womb.217See Jeremiah 1:5. So also [the name] Gog218Ezekiel 39:1. was one by which all the princes of Magog were called.
Thus Balaam added with this third prophecy of his [to his previous two prophecies] by telling Balak that Jacob’s tents are goodly,219Verse 5. referring to the period from the time that they were dwellers in tents until they would inherit the land [of Canaan], and the dwellings of Israel219Verse 5. after the conquest and division of the Land will also be good, meaning that they will dwell therein in safe habitations. And [Balaam further informed Balak that] Israel’s land will be full of all goodly things, like a watered garden, and like a spring of water, whose waters fail not,220Isaiah 58:11. and that Israel will conquer Amalek because he attacked him, and will destroy his memory; and that the kingdom of Israel will be even more exalted,221Verse 7. because they will have afterwards mighty kings, who will be exceedingly elevated. And he further told him that Israel would eat up his adversaries and break their bones in pieces,222Verse 8. referring to their wealth and all their belongings. And [finally, in Verse 9] he told him that Israel would dwell in the Land safely, fearing no people, as a lion, and as a lioness that does not fear any ravenous beast.223Isaiah 35:9. And so now Balak despaired of [ever fighting] Israel, for [he realized that] if he would fight against him, he would be truly destroyed, for Israel would eat up all his adversaries222Verse 8. in the same way that he would destroy Amalek because he attacked him. Therefore Balak now told Balaam to flee to his place,224Verse 11. for he has no more desire for him [and his counsel].
It is possible that every king of the Amalekite people was called Agag, because the first king whom they set up over them was so called [Agag], and thus all his descendants who occupied his throne were called by his name,215Thus there is no need to say, as Rashi did, that Agag here refers to the specific Amalekite king of King Saul’s days, and that his name is foretold a few hundred years before he was born, as Scripture would not foretell the birth of a wicked man. as are most kings even nowadays, who are called by the name of those who [originally] seized the kingdom. So also Haman the Agagite216Esther 3:1. [was so called] because he was a descendant of that royal family. For it is unlikely that the prophet [Balaam] would cite the name of a wicked man [Agag] even before he was formed in the womb.217See Jeremiah 1:5. So also [the name] Gog218Ezekiel 39:1. was one by which all the princes of Magog were called.
Thus Balaam added with this third prophecy of his [to his previous two prophecies] by telling Balak that Jacob’s tents are goodly,219Verse 5. referring to the period from the time that they were dwellers in tents until they would inherit the land [of Canaan], and the dwellings of Israel219Verse 5. after the conquest and division of the Land will also be good, meaning that they will dwell therein in safe habitations. And [Balaam further informed Balak that] Israel’s land will be full of all goodly things, like a watered garden, and like a spring of water, whose waters fail not,220Isaiah 58:11. and that Israel will conquer Amalek because he attacked him, and will destroy his memory; and that the kingdom of Israel will be even more exalted,221Verse 7. because they will have afterwards mighty kings, who will be exceedingly elevated. And he further told him that Israel would eat up his adversaries and break their bones in pieces,222Verse 8. referring to their wealth and all their belongings. And [finally, in Verse 9] he told him that Israel would dwell in the Land safely, fearing no people, as a lion, and as a lioness that does not fear any ravenous beast.223Isaiah 35:9. And so now Balak despaired of [ever fighting] Israel, for [he realized that] if he would fight against him, he would be truly destroyed, for Israel would eat up all his adversaries222Verse 8. in the same way that he would destroy Amalek because he attacked him. Therefore Balak now told Balaam to flee to his place,224Verse 11. for he has no more desire for him [and his counsel].
Sforno
על עין המים, she was engaged in prayer. Compare Pessachim 11 where the words of the angel in verse 11 כי שמע ה' אל עניך "for the Lord has heard your affliction" are understood as referring to Hagar's prayer prior to her receiving this vision.
Rashi
'ויאמר לה מלאך ה' וגו AND THE ANGEL OF THE LORD SAID UNTO HER etc. (see also Genesis 16:10 & Genesis 16:11). For each statement (in these three verses) a different angel was sent to her, and this explains why in reference to each statement the phrase is used, “and an angel said to her” (Genesis Rabbah 45:7).