| 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.
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| 12. | The position of this tower, situated upon an exterior angle, may indicate that the building was of a Z-plan construction.
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| 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:
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| 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:
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| 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.
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| 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.
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| 17. | In a cyclic polygon, longer sides correspond to larger exterior angles in the dual ( a tangential polygon ), and shorter sides to smaller angles.
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| 18. | Now the interior angle of the triangle " OPR " at O is one third of the triangle's exterior angle at " R ".
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| 19. | Since the interior and exterior angles sum to 180 degrees, the angle " CPD " is exactly 90 degrees, i . e ., a right angle.
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| 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?
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