Definition of engages:
(v) :
(transitive) To engross or hold the attention of; to keep busy or occupied.
(v) :
To interact socially.
(v) :
(ambitransitive) To draw into conversation.
(v) :
(transitive) To enter into conflict with (an enemy).
(v) :
(intransitive) To enter into battle.
(v) :
(transitive) To arrange to employ or use (a worker, a space, etc.).