[br]In other words: Given any triangle ABC, the sum of any of[br]the two inner angles is less than two right angles.[br][br][br]

1. Given triangle ABC with angles [math]\alpha[/math], [math]\beta[/math], and [math]\gamma[/math].[br]2. Extend line BD to point D, with external angle [math]\delta[/math].[br]3. The sum of the angles ACB and ACD are equal to two right angles (I.13).[br]4. The angle ACD is greater than either angle ABC or CAB (I.16).[br]5. Add the same value (angle ACB) to both sides of each inequality.[br]6. Therefore, the sum of either ABC or CAB with angle ACB will be less than 180[math]^o[/math] (or 2 right angles).[br]Q.E.D.