IPA: /ɪnˈɡeɪdʒd/
KK: /ɪnˈɡeɪdʒd/
Having made a commitment to someone or something, often in a romantic context, or being busy with a task or activity.
They are engaged to be married next summer.
Engaged is formed from "en-" (meaning to cause to be in) and "gage" (from Old French *gage*, meaning a pledge or promise). The word "engaged" means to be in a state of commitment or to be pledged to something.
Think of being 'caused to be in' a 'pledge' — that's why engaged means being committed or promised to someone or something.