For any triangle,  (the sum of) two angles taken together in any (possible way) is less than two right-angles. Let $ABC$ be a triangle. I say that (the sum of) two angles of triangle $ABC$ taken together in any (possible way) is less than two right-angles. <prf> Thus, (the sum of) $ABC$ and $BCA$ is less than two right-angles. Similarly, we can show that (the sum of) $BAC$ and $ACB$ is also less than two right-angles, and further (that the sum of) $CAB$ and $ABC$ (is less than two right-angles).Thus, for any triangle,  (the sum of) two angles taken together in any (possible way) is less than two right-angles.