PRINCIPIA · THEOREM

Exterior angle equals the sum of two non-adjacent interior angles

Dependencies: Triangle interior angles sum to 180°, Linear pair sums to 180°.

Statement

Let $\triangle ABC$ have side $BC$ extended along its original direction to a point $D$ (so that $C$ lies between $B$ and $D$ ). Call $\angle ACD$ the exterior angle of $\triangle ABC$ at vertex $C$ , denoted $\gamma'$ . Then

\gamma' = \angle A + \angle B.

$Exterior-angle identity: in \triangle ABC, extend BC to D; the exterior angle \gamma' is exactly tiled by \alpha + \beta$

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