engaged

be

deeply, heavily

My daughter is deeply engaged in her new job and loves going to work every day.

fully, totally

largely, mainly, primarily

directly

constantly

currently

actively, busily

otherwise

My manager was otherwise engaged in meetings all afternoon, so we rescheduled for tomorrow.

in

The children were engaged in building a sandcastle at the beach.

on

She remained deeply engaged on the community garden initiative throughout the year.

with

My daughter was engaged with her homework for three hours yesterday afternoon.

be

become, get

They became engaged after dating for three years.

to

My brother is engaged to a teacher who works at the local primary school.