engaged in WordNet English dictionary

1. reserved in advance
   booked  engaged  set-aside 
   
2. (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"
   busy  engaged  in use 
   
3. built against or attached to a wall
   "engaged columns"
   engaged 
   
4. having services contracted for
   "the carpenter engaged (or employed) for the job is sick"
   engaged 
   
5. (used of toothed parts or gears) interlocked and interacting
   "the gears are engaged"; "meshed gears"; "intermeshed twin rotors"
   engaged  meshed  intermeshed 
   
6. involved in military hostilities
   "the desperately engaged ships continued the fight"
   engaged 
   
7. having ones attention or mind or energy engaged
   "she keeps herself fully occupied with volunteer activities"; "deeply engaged in conversation"
   engaged  occupied