What do i do with a big angel and a newly added small angel fish?

I had an angel fish for about a month and it grew to 3 inches from top to bottom. Now i went to a fish store and bought another angel about 1 inches. When i put my small angel in the big one would chase it around and try to bite the small angel fins. I really want to put that small angel in but I should i do? The angel stays fine with 2 tetra and a platy but i don't know why it only attack the small angel fish. Any help would be appreciated