engaged
en-gaged
adjective
Actively involved in or committed to a particular activity or cause.
"She is deeply engaged in her research."
adjective
Having formally agreed to marry someone; betrothed.
"They got engaged last Christmas."
adjective
Busy doing something, or unavailable because it is in use.
"The phone line is engaged."
Thesaurus
Synonyms: set-aside, reserved, booked, geared, intermeshed, meshed, bespoken, committed, betrothed, attached, occupied, busy