1. [verb] Simple past tense and past participle of engage
2. [adjective] Agreed to be married.
3. [adjective] Busy or employed.
4. [adjective] (British) (of a telephone) Already involved in a telephone call when a third party calls
5. [adjective] (architecture) (of a column) attached to a wall or sunk into it halfway
6. [adjective] (of gears or cogs) in contact and in operation
7. [adjective] (military) being attacked or attacking
8. [adjective] Having ones attention or mind or energy engaged; 'she keeps herself fully occupied with volunteer activities'; 'deeply engaged in conversation'.
9. [adjective] Involved in military hostilities; 'the desperately engaged ships continued the fight'.
10. [adjective] Reserved in advance.
11. [adjective] (of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line); 'her line is busy'; 'receptionists' telephones are always engaged'; 'the lavatory is in use'; 'kept getting a busy signal'.
12. [adjective] (used of toothed parts or gears) interlocked and interacting; 'the gears are engaged'; 'meshed gears'; 'intermeshed twin rotors'.
13. [adjective] Having services contracted for; 'the carpenter engaged (or employed) for the job is sick'.
14. [adjective] Built against or attached to a wall; 'engaged columns'.