verb
-gages; -gaged; -gaging
[+ obj] formal :to hire (someone) to perform a particular service
[+ obj] :to get and keep (someone's attention, interest, etc.)
to start fighting against (an opponent) [+ obj]
to move (a mechanism or part of a machine) so that it fits into another part [+ obj]
engage in
[phrasal verb]
engage in (something) :to do (something)
engage (someone) in (something) :to cause (someone) to take part in (something)
engage with
[phrasal verb]
engage with (someone or something) formal :to give serious attention to (someone or something)