From Latin 'angulus' (corner), from PIE *h₂engʷ- (to bend) — the same root that gave us 'ankle,' 'anchor,' and 'angler,' all things that bend.
The space between two intersecting lines or surfaces at or close to the point where they meet, measured in degrees; a particular way of approaching or considering an issue or problem; a corner or projecting point.
From Old French angle, from Latin angulus ("corner, angle"), from PIE *h₂enk- ("to bend"), a root of remarkable productivity across Indo-European. From *h₂enk- descend: Latin ancus ("having crooked arms"), Greek ἀγκών (ankṓn, "elbow, bend"), ἄγκυρα (ánkyra, "anchor" — the hooked implement), Sanskrit aṅká- ("hook, bend"), and Old English ancleo ("ankle" — the bending joint). The English word ankle is thus a distant cousin of angle, both encoding the concept of bending. The geometric sense — the figure formed
The geometric word 'angle' and the fishing word 'angler' both descend from the same Proto-Indo-European root meaning 'to bend.' A fishhook (Old English 'angel') is a bent piece of metal, and an angle is where a line bends. The Angles — the Germanic tribe that gave England its name — were supposedly named after the hook-shaped Angeln peninsula in Schleswig.