The [[addition|sum]] of the [[interior angles]] of a plane [[Triangle]] must be $180^\circ$ Most easily proved by combining knowledge of [[supplementary angles]] and [[Sum of Exterior Angles]] If a triangle has interior angles $\alpha^\circ, \beta^\circ, \gamma^\circ$ then it has corresponding exterior angles $(180-\alpha)^\circ$, $(180-\beta)^\circ$, $(180-\gamma)^\circ$. The sum of these is $(540-\alpha-\beta-\gamma)^\circ=360^\circ$, which solves to $(\alpha+\beta+\gamma)^\circ=180^\circ$