The Quran does not teach the belief that Jibreel (Gabriel) was an angel. Jibreel is mentioned three times in the Quran by name, and twice he is mentioned separately from the angels:
مَن كانَ عَدُوًّا لِلَّهِ وَمَلائِكَتِهِ وَرُسُلِهِ وَجِبريلَ وَميكالَ فَإِنَّ اللَّهَ عَدُوٌّ لِلكافِرينَ
man kaana ʿaduwwan li-llaahi wa-malaaʾikatihī wa-rusulihī wa-jibrīla wa-mīkaala fa-ʾinna llaaha ʿaduwwun li-l-kaafirīn
‘Whoever is an enemy of Allah, His angels and His messengers, and Gabriel and Michael; Allah is indeed the enemy to the disbelievers.’
And in Surah at-Tahrim 66:4:
إِن تَتوبا إِلَى اللَّهِ فَقَد صَغَت قُلوبُكُما ۖ وَإِن تَظاهَرا عَلَيهِ فَإِنَّ اللَّهَ هُوَ مَولاهُ وَجِبريلُ وَصالِحُ المُؤمِنينَ ۖ وَالمَلائِكَةُ بَعدَ ذٰلِكَ ظَهيرٌ
ʾin tatūbā ʾilā llāhi fa-qad ṣaghat qulūbukumā wa-ʾin taẓāharā ʿalayhi fa-ʾinna llāha huwa mawlāhu wa-jibrīlu wa-ṣāliḥu l-muʾminīna wa-l-malāʾikatu baʿda dhālika ẓahīr
If you both turn to Allah, then indeed your hearts are already inclined; and if you back up each other against him, then surely Allah it is who is his Guardian, and Jibreel and -the believers that do good, and the angels after that are the aiders.
Both of these ayaat isolate Jibreel from the angels. However, one can say to mention Jibreel separately shows his special status. This could be true if there was support for this statement.
Also, we should note in other verses, Allah differentiates between “Ruh” and “al-Malaikat” or the Angels:
يَومَ يَقومُ الرّوحُ وَالمَلائِكَةُ صَفًّا ۖ لا يَتَكَلَّمونَ إِلّا مَن أَذِنَ لَهُ الرَّحمٰنُ وَقالَ صَوابًا
yawma yaqūmu r-rūḥu wa-l-malāʾikatu ṣaffan lā yatakallamūna ʾillā man ʾadhina lahu r-raḥmānu wa-qāla ṣawāba
The Day that the Spirit/ar-Ruh and the angels/al-Malaaikat will stand in rows, they will not speak except for one whom the Most Merciful permits, and he will say what is correct.
This distinction between “Ruh” and the angels can be read in other parts of the Quran = an-Nahl 16:2, al-Ma’arij 70:4, al-Qadr 97:4. So we have four verses as evidence of “Ruh” not being from the angels.
Now, a well-known belief exists among certain sects that Jibreel is indeed “Ruh al-Qudus;” since Allah mentions in Surah al-Baqara 2:97 that “…Jibreel…brought/nazzala (the revelation?) to your heart…” and also in Surah an-Nahl 16:102 in similar wording except “nazzala” is connected to “Ruh al-Qudus“
If this is true -Jibreel is Ruh al-Qudus- then this further shows Jibreel “Ruh al-Qudus” was not an angel but in fact something different.
In Sahih Muslim there is a single narrative attributed to ‘Aaisha reporting Rasolullah allegedly said:
…خُلِقَتِ الْمَلاَئِكَةُ مِنْ نُورٍ
“The angels were created from light/noor…”
Allah says about the “Ruh”: