The Bible nowhere explicitly describes Satan as an angel before he rebelled against God and was cast out of heaven. Assuming Ezekiel 28:12–18 is symbolic of Satan’s fall, Satan is described as a “guardian cherub.” Cherubs are angelic creatures, possibly the highest order of angels. So, in that sense, yes, Satan was an angel.
Job 1:6–7 describes Satan appearing before God with the other “sons of God,” very likely a reference to the angels. Matthew 25:41 mentions “the devil and his angels.” Revelation 12:7, describing the end-times war in heaven, says, “Michael [the archangel] and his angels fought against the dragon [Satan] and his angels.” Whether or not Satan is technically an angel is beside the point. Satan is an angelic-type creature with a close connection to the angels.
Why would Satan, an angel, rebel against God? According to Isaiah 14:12–14 (another symbolic description), Satan rebelled against God because of pride. Satan did not want to be the most beautiful or most powerful angel. Satan wanted to be God. Satan did not want to worship God. Satan wanted to be worshiped. So, Satan rebelled and became the fallen angel we now know as the devil. His fate will be eternity in the lake of fire (Revelation 20:10).