Yes, Muslims do believe in Angels - belief in angels is one of the 6 pillars of Islamic faith.
However, the Islamic beliefs regarding Angels differ from those of Christianity in Judaism. Some potential differences/ beliefs of Muslims regarding angels are:
Unlike humans which are described in Islam to be made from black sticky clay, God teaches us that Angels are created from Pure Light (Noor).
Angels are servants/agents of God. Angels are created by God; therefore, they are not divine and should not be worshipped.
Muslims do not believe that angels have free will -- they are incapable of disobedience. However, they are intelligent and can ask questions of God (e.g. Al-Baqarah 2:30)
Angels have no gender nor child form.
Angels can take on human form though that is not their natural form. The Quran mentions how at the moment of Jesus’ conception, God sent Gabriel(The Archangel) to Mary in the form of a man.
Satan/Lucifer was not a fallen angel -- he was from a separate creation called the jinn.
Muslims believe that for each person, there is an angel on their right side and an angel on their left side that document their good deeds and bad deeds. Their job is recording, not encouraging particular actions.
They do not eat or drink and the angels do not get bored or tired of worshipping God.
Some angels have specific roles, e.g: The Angel of Death: Azrael, Guardian of Hell: Malik among others.
The commonly portrayed image of angels being human like creations with wings instead of arms is something that Muslims cannot confirm nor deny as there has not been given a visual description of Angels in Islam and neither has anyone seen them in their original form.