Although this brings up more important questions and contradictions, the most obvious answer is yes, angels can sin.
Had God not created Satan with the intent of a rebellion, humanity would not have learned right from wrong.
If humanity had never done this, than there would be no reason for Jesus to die or for us to worship a god.
If there's no reason for us to worship a god, the god may as well not exist.
Since the very jealous and proud God wants worship, he created angels that he knew would defy him, thus laying the groundwork for sinning.
It says it in the Bible. Satan was an angel before, so obviously he did something wrong. As a child growing up, my teachers would tell me that Heaven is perfect and therefore we cannot sin in heaven, making it the most holy place. So why would God allow his angels to sin?
Angels are no more likely to be real than vampires, werewolves and ghosts. These are just story characters that have been made up to try to explain things in the past when human knowledge was limited. There is no point discussing them. The bible is just another work of ancient fiction, there is no point referring to it because it is just a collection of old stories which are not true.