1.Definition: (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)

"Receptionists' telephones are always engaged"

Related Adjective(s):busy

2.Definition: (used of toothed parts or gears) interlocked and interacting

"The gears are engaged"

Related Adjective(s):intermeshed, meshed

3.Definition: built against or attached to a wall

"Engaged columns"

4.Definition: having ones attention or mind or energy engaged

"Deeply engaged in conversation"

Related Adjective(s):occupied

5.Definition: having services contracted for

"The carpenter engaged (or employed) for the job is sick"

6.Definition: involved in military hostilities

"The desperately engaged ships continued the fight"

7.Definition: reserved in advance

Related Adjective(s):booked