How do cougars protect themselves from predators?
The only real predators that cougars have are humans with dogs and guns; they deal with those by running and hiding, generally, and often take refuge high in trees. They may also come into conflict with wolves or bears, over prey; a cougar will generally back down from a bear, and would probably back down from a wolfpack as well.
Sub-adult cougars have problems from jaguars, bears, wolves, wolverines, and more mature cougars; all of whom may dispatch the cat from his kill or wound him in a confrontation. But apparently, a mother puma with cubs or a fully mature male with an established territory will take these foes on in toe-to-toe battle when pushed to do so, and usually come away the victor. The exception to this seems to be a wolf pack-the cat is at a disadvantage when facing more than one wolf and will retreat to the nearest tree-top.