What's in a word-piece?
Greek -gon derives from Indo-European genu-, 'knee, angle.' That bent knee is a concrete, bodily representation of the idea that early mathematicians needed to express.
Reference to bones and the angles between them appears in other descriptions of geometric ideas, as well. We speak of the "legs" of a triangle. And the -scel- part of isosceles, referring to those legs, appears in the familiar English word skeleton! Algebra derives from Arabic, rather than Greek, but also refers to bones!
Not only does Indo-European genu- give the gn that becomes kn in knee, but it appears whole in genuine (honest, on bended knee) and genuflect (to bend the knees).
Related mathematical terms
* For terms that use the word-part -gon, see: Hexagon, Octagon, Polygon, Diagonal, Orthogonal, Trigonometry