Rear wheel rubs frame after tire change
You've lost the derailleur hanger mounting nut. Don't worry, they're dead cheap. Without it the hanger won't stay in place without the wheel nuts done up tight. You can get away without one (see matt's answer), but it's not ideal. It's better and less fiddly to use a proper mounting nut:





The way you've set it up now is totally wrong - the triangle-shaped hole is just a cutout in the rear dropout - it isn't designed to have anything mounted to it. I presume the other hole of which you speak is a mudguard or rack mounting eye.