"having five angles," 1650s, from Late Latin quinquangulus "five-cornered," from quinque "five" (from PIE root *penkwe- "five") + angulus "angle" (see angle (n.)). Quinquangle (n.) "pentagon" is attested from 1660s.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit panca, Greek pente, Latin quinque, Old Church Slavonic pęti, Lithuanian penki, Old Welsh pimp, Old English fif, Dutch vijf, Old High German funf.
"space or difference in direction between intersecting lines," late 14c., from Old French angle "an angle, a corner" (12c.) and directly from Latin angulus "an angle, a corner," a diminutive form from PIE root *ang-/*ank- "to bend" (source also of Greek ankylos "bent, crooked," Latin ang(u)ere "to compress in a bend, fold, strangle;" Old Church Slavonic aglu "corner;" Lithuanian anka "loop;" Sanskrit ankah "hook, bent," angam "limb;" Old English ancleo "ankle;" Old High German ango "hook").
Figurative sense "point or direction from which one approaches something" is from 1872. Angle-bracket is 1781 in carpentry; 1956 in typography.
<a href="https://www.etymonline.com/word/quinquangular">Etymology of quinquangular by etymonline</a>
Harper, D. (n.d.). Etymology of quinquangular. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/quinquangular