Using the small hole that missed the stud, unbend a wire hanger and fish it in the hole sideways until you hit a stud. Mark the hanger and pull it out and measure that distance on the face of the wall. Repeat in opposite direction to find adjacent stud. Measure in between two to find the stud spacing down the wall. Some homes were built with balloon framing which is generally 24" spacing rather than the now typical 16".