角 is a drawing of an animal's horn — the inner diagonal marks the grain etched into it. Horn is the original sense; from the horn's sharp angularity grew "corner, angle," and the geometric "angle" formed where two sides meet.

Mandarin: jiǎo, 3rd tone (horn, angle, corner). But when it means an actor's "role" it is read jué — 角色 (juésè, a role), 主角 (zhǔjué, leading role). A one-character, two-sounds case. 三角形 (sānjiǎoxíng, triangle), 角度 (jiǎodù, angle / degree). It is also a literary currency unit, one-tenth of a yuan — 角 (jiǎo).

Japanese: on-reading カク (kaku), kun つの (tsuno, horn) and かど (kado, corner). 三角 (sankaku, triangle), 角度 (kakudo, angle), 角 (tsuno, horn), 街角 (machikado, street corner). The world of sumo wrestling is called 角界 (kakukai).

Korean hanja-sound "gak": 角度 (gakdo, angle), 三角形 (samgakhyeong, triangle), 直角 (jikgak, right angle), 頭角 (dugak, prominence — "showing one's horns"). Every 角 of school mathematics is this character.

Memory aid: an animal's horn with its grain etched in — from its sharp angularity comes "angle."