The Magical Girlfriend is a common trope of anime. Basically, normal nerd boy gets a magical girlfriend. On the plus side she can get him out of jams. On the negative side, she tends to get him into jams by being insanely jealous and having odd friends/old lovers/family.
An angel makes for a very unusual girlfriend. In "Tenshi Ni Narumon" (I wanna be an angel) our hero meets a young girl who indeeds wants to be an angel, and her odd family of monsters. They are often attacked by other people of their world who seem to have invented "Rubber tech." It's all mostly light hearted and very fun.
He had it easy. Our hero in Dokuro chan is also sort of dating an angel. I say sort of because it's not his idea. She has latched on to him for reasons all her own. Worse, she has a bad temper and will KILL him on a whim. It's all ok though, cause then she just brings him back to life. What fun!