(i) Carry out or participate in an activity; be involved in: ‘They engaged in a discussion’ (ii) Consume all of one's attention or time: ‘Her interest in books engages her completely.’ (iii) Start in a job or pay to do a particular piece of work: ‘They engaged two new secretaries in the department.’(iv) Be/get engaged: ‘When did you get engaged?’ ‘We were engaged for almost a year before we got married.’
Engaged
(i)Be/get engaged to sb: ‘When we first met, she was already engaged to an airline pilot.’ (ii) Having one's attention, mind or energy occupied: ‘He is deeply engaged in conversation.’ (iii) Reserved in advance: ‘Three or four of these highway lanes must be engaged for passenger cars only’. (iv) (Of facilities such as telephones) unavailable for use by anyone else or indicating unavailability: ‘His telephone numbers are always engaged.’