A pack of collared "pet" dogs killed my family's billy goat. We didn't have a gun when we found the goat but had heard the pack and went to check on the goat out in the Orchard. They had basically tore all the skin and muscle meat out of his left rear hind quarters and he was laying there in agony. I would have shot every one of those @#$%ing dogs without a second's remorse.
Growing up on the farm, it was a standing unwritten rule that a single roaming dog could be shot on sight. However, we all typically gave the dog one chance, and word got back to the owner about the roaming. That usually solved it.
Any two or more dogs roaming would be shot on sight. No hard feelings. Period. We all knew the rules and the situation with pack dogs and the destruction they do, whether to our livestock or wild animals.