This is a touchy subject! I don't think that I could shoot a dog unless I felt there was danger for me, my family or friends, or my pets. You must control your animals even when you own a lot of property. There's no excuse to let them run free because you don't know what will happen if they stray too far.
Near where I work there was an incident recently where two large dogs were splitting a doe apart in the yard of a very populated residential area. This was discovered by an old woman who screamed and attracted the attention of her family, including a small child. If these dogs could do this to a deer just think what could happen to a child if these dogs were somehow provoked.
My neighbors have a Doberman and a Pit Bull that they only let out to do their business. When I am walking in the field below their property I am always afraid that they are going to spot me and attack. If you would drive up to their house there is no way that you could get out of your car without these dogs attacking you. If the dogs would come onto my property I would scare the dogs away with a pellet gun and then approach the owner. If it happened again then I would choose a larger weapon.
If these dogs are pets then they shouldn't be running wild.
I'm an animal lover (one dog & 3 cats) and a hunter.