IPA: //deɪˈɡeɪ//
KK: /deɡeɪ/
Not restricted or limited; relaxed and easy in manner or style.
She walked into the room with a dégagé attitude, making everyone feel at ease.
Dégagé is derived from the French word "dégager" (meaning to free or to release), which is formed from the prefix "dé-" (meaning to remove or reverse) and the root "gager" (meaning to pledge or to guarantee). The term originally conveys the idea of freeing oneself from a pledge or obligation.
Think of 'removing' ('dé-') a 'pledge' ('gager') to remember that dégagé means to be free or unencumbered.