"skin disease of hairy animals," especially dogs, often caused by mites, c. 1400, manjeue, maniewe, from Old French manjue, mangeue "the itch," also "hunger, appetite; itching, longing," literally "the eating," verbal noun from a collateral form of Old French mangier "to eat" (Modern French manger) "to eat," from Late Latin manducare "to chew, eat," from manducus "glutton," from Latin mandere "to chew" (see mandible).
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
<a href="https://www.etymonline.com/word/mangy">Etymology of mangy by etymonline</a>
Harper, D. (n.d.). Etymology of mangy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/mangy