engaged
Engaged is the past participle of engage and functions as an adjective with several related meanings. As a verb, engage means to occupy, involve, or hire someone, or to pledge or commit someone to a course of action. In the sense of marriage, to be engaged means to have promised to marry a partner. As an adjective, engaged describes someone who is involved in a task or activity, or something that is in operation or connected to another component, such as a gear that is engaged.
Etymology: The word derives from Old French engager, from gage "pledge." The early sense centered on pledges
Usage: In everyday speech, “the line is engaged” means the telephone line is busy; “I am engaged