lay your mirror down on the carpet face down. then stretch the wire hanger as it would be if on the wall. have the angle where the fastener would be and have the wire there. When there, trace the wire on the back of the mirror backing.
Now, get a thumb tack and place it where the top angle is located and tape it securely to the back of the mirror with the tack's point to the wall. Now carefully place the mirror on the wall where its intended to be and when there push on the mirror where the tack is located to depress a pointed mark. Remove the mirror find the tack hole and there drill your anchor hole. you might want to go a bit higher up due to the stretching of the wire hanger.
If finding the hole is difficult put some red lipstick on the point and there is the spot, this works if you do not pre touch it to the wall.
see what your doing? tracing a tight line is the key because the weight of the mirror will cause the line to stretch and you need to account for that.