In the Wikipedia page on Islamic views of angels, it's mentioned that they're messengers with wings.
Does Islam offer an explanation for the purpose behind these wings?
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Praise be to Allah, Who created (out of nothing) the heavens and the earth, Who made the angels, messengers with wings,- two, or three, or four (pairs)
— The Holy Quran, Chapter 35 (Fatir), Verse 1
But again from the hadith we can find that Gabriel has 600 wings:
Narrated Abu Ishaq-Ash-Shaibani: I asked Zir bin Hubaish regarding the Statement of Allah: "And was at a distance Of but two bow-lengths Or (even) nearer; So did (Allah) convey The Inspiration to His slave (Gabriel) and then he (Gabriel) Conveyed (that to Muhammad). (53.9-10) On that, Zir said, "Ibn Mas'ud informed us that the Prophet had seen Gabriel having 600 wings." —Muhammad al-Bukhari, Sahih al-Bukhari, Volume 4, Book 54, Number 455
So the crux of the matter we can find from the same verse of 35:1
He increases in creation what He wills. Indeed, Allah is over all things competent. (35:1)
It doesn't matter that how many wings they have or why they have wings but what matter is Allah has set some examples for us to understand his greatness, knowledge,power whatever.
We must distinct between the language of Quran and ordinary language.when Quran describes angeles in such a cases we have to notice the symbolic language. angels are immaterial and perfect. Quran try to draw angels by this kind of language .