Exterior angle inequality

Dependencies: Vertical angles are equal, SAS congruence, Ruler axiom, Protractor axiom. This is Euclid I.16, and does not depend on the parallel postulate — it is a "neutral geometry" result.

Statement

Let $\triangle ABC$ be non-degenerate. Extend side $BC$ beyond $C$ to a point $D$, obtaining the exterior angle $\angle ACD$ at $C$. Then any exterior angle is strictly greater than any non-adjacent interior angle:

Note that this is a strict inequality — only after the parallel postulate is added can it be upgraded to the equality $\angle ACD = \angle BAC + \angle ABC$ (Exterior angle equals the sum of two non-adjacent interior angles); that's an L3 affair.