11. Then one of the alternate angles is an exterior angle equal to the other angle which is an opposite interior angle in the triangle. 12. The position of this tower, situated upon an exterior angle , may indicate that the building was of a Z-plan construction. 13. By Euclid's exterior angle theorem, any exterior angle of a triangle is greater than either of the interior angles at the opposite vertices: 14. By Euclid's exterior angle theorem, any exterior angle of a triangle is greater than either of the interior angles at the opposite vertices: 15. Pasch's axiom and the exterior angle theorem still hold for an omega triangle, defined by two points in hyperbolic space and an omega point. 16. Therefore, it would make sense for a 180 degree angle to have an interior angle of 180 degrees, and an exterior angle of 0 degrees. 17. In a cyclic polygon, longer sides correspond to larger exterior angles in the dual ( a tangential polygon ), and shorter sides to smaller angles. 18. Now the interior angle of the triangle " OPR " at O is one third of the triangle's exterior angle at " R ". 19. Since the interior and exterior angles sum to 180 degrees, the angle " CPD " is exactly 90 degrees, i . e ., a right angle. 20. Clearly, the sum of angles on the " outside " now is 180?and at each vertex, the sum of the interior angle and exterior angle is 360?
