A locking system wherein the latch is rotatable to provide either a first beveled surface for use as a ramp in latching or a second beveled surface for use as a ramp in unlatching. An entire latch module may be rotated about its axis by a rotary solenoid to achieve this function, and the first and second ramping surfaces are physically the same surface repositioned by rotation 180°. Alternatively, a releasable latch has a beveled surface for engaging a striker plate during bolt entry and a non-beveled surface for locking. The latch is pivotable to allow the non-beveled surface to become the beveled ramp for unlocking. The releasably pivotable latch mechanism may be used with a deadlock. The mechanism is readily incorporated into a rim exit device for releasably securing a door such as an emergency exit and may be actuated either electrically or manually.