The following nail trim information is shared with permission from:

Most people when cutting nails try to cut directly across the dog’s nail (as in the diagram below).  However, as Dr. Leslie recommends the best way to cut your dog’s nails without hurting them, and to get that quick to recede, is to cut the sides of the nails on angling back.

You can find more details about this method from Susan Garrett and
Dr. Leslie Woodcock DVM at https://susangarrettdogagility.com/2013/08/cutting-your-dogs-nails-how-important-is-it-really and DogsThat.com