In any triangle two angles taken together in any manner are less than two right angles.

Let $ABC$ be a triangle;I say that two angles of the triangle $ABC$ taken together in any manner are less than two right angles.For let $BC$ be produced to $D$. [Post. 2]Then, since the angle $ACD$ is an exterior angle of the triangle $ABC$,it is greater than the interior and opposite angle $ABC$. [Prop. 1.16]Let the angle $ACB$ be added to each;therefore the angles $ACD$, $ACB$ are greater than the angles $ABC$, $BCA$.But the angles $ACD$, $ACB$ are equal to two right angles. [Prop. 1.13]Therefore the angles $ABC$, $BCA$ are less than two right angles.Similarly we can prove that the angles $BAC$, $ACB$ are also less than two right angles, and so are the angles $CAB$, $ABC$ as well.Therefore etc.Q.E.D.