An adapter for mounting a luminaire to a track of a track lighting system includes a main body and a head having axes that are angled with respect to each other. The head is configured to be insertable into the track and rotatable to align the adapter body with the track ant to make electrical contact with conductors within the track. The rotation required is less than 70 degrees, and may be as little as 13 degrees or less, enabling installation of track lighting near obstructions.