engaged in something Definition

1. Bound by a promise to marry them.

Thesaurus: betrothed, pledged, promised, spoken for, unavailable, committed, bound.
Form: engaged to someone (usually)
2. Said of a room or a telephone line, etc: not free or vacant; occupied; in use.
3. Geared together; interlocked.

Busy or occupied with it.
Thesaurus: busy with, working with, occupied with, employed with, preoccupied with, tied up with; interested in, engrossed in, involved in, absorbed in, immersed in.