The nest needs to be in a box. Especially in a wire cage.
Use a shoe box or something of similar size. It needs to be big enough for mom to get in and turn around but not big enough to lie down in.
Put an inch or two of shavings or soft absorbent litter into the bottom of the box. If you don't have shavings, don't worry too much about this step, you can just use hay or straw.
Fill the box with hay or straw and compact in quite tightly. Make a fist sized hole in the middle of the box, and transfer the babies and as much of the original nest as you can.
Make sure they have lots of fur covering them. Because she is an angora, you should cut any fur into shorter lengths of about 1 inch so that the babies cannot strangle themselves in it.
I would remove the towel. If a thread comes lose on the towel from mom or the babies chewing on it, one of the babies can become tangle in it and can strangle or lose a limb.
The babies will stay nice and warm if they are in a nice nest box with lots of fur. They will cuddle together and the fur will insulate them.
Mom should feed them with in the first 24 hours of birth. If you can post pictures of the babies, we can tell you if they look fed or not.
Mom will not eat them if you touch them. That is a myth. Mom's instincts to care for the babies are stronger than any discomfort from a strange smell. Plus, she knows you so your scent is not strange. If you are still concerned you can just make sure you rub your hands on her before touching the babies so your hands smell like her.
Also, make sure the male is separated. If he wasn't separated, she is pregnant again and will give birth before this litter is ready to wean and reduces their chances of surviving to weaning age.
-Dawn
