Belief in angels is one of the six articles of faith. The believers are described in the Quran as those who affirm them:
"All of them have believed in Allah and His angels and His books and His messengers."
— Quran 2:285 (Saheeh International)1
What angels are
Angels are beings God created to serve and obey Him perfectly. The Prophet Muhammad ﷺ described their origin:
"The angels were created from light, the jinn were created from a smokeless flame of fire, and Adam was created from what has been described to you."
— Sahih Muslim 29964
Unlike human beings, angels have no free will to disobey:
"[Over the Fire] are angels, harsh and severe; they do not disobey Allah in what He commands them but do what they are commanded."
— Quran 66:6 (Saheeh International)2
What angels do
The Quran describes angels carrying out many tasks by God's command.567 The greatest of these is the delivery of revelation: it was the angel Jibril (Gabriel) who brought the Quran to the Prophet ﷺ. Others are charged with recording each person's deeds:
"And indeed, [appointed] over you are keepers, noble and recording; they know whatever you do."
— Quran 82:10-12 (Saheeh International)3
Among the angels named or known in Islamic tradition are Jibril (revelation), Mika'il (Michael), and Israfil, who will sound the trumpet on the Last Day.
In short
Muslims believe in angels as a matter of faith: beings created from light who never disobey God and who carry out His commands throughout creation — from bringing revelation to the prophets to recording the deeds of every human being.