I tried keeping a betta in with my angel (back when I didn't know angels were nippers) and as soon as I put the betta in, my angel immediately went after my poor betta and started nipping his tail, so I took the betta out right away.
Hmm...I wouldn't keep a Male Betta with Angelfish, for the same reason as people have said above. The nipping. However, my female Betta has been living with my Angelfish for about a year now, and they are best friends. They eat together, swim together, play together...etc.