| 1. | A 120 degree angle has an interior angle of 120 and an exterior angle of 60.
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| 2. | A 150 degree angle has an interior angle of 150 and an exterior angle of 30.
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| 3. | The exterior angle theorem is not valid in spherical geometry nor in the related elliptical geometry.
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| 4. | One interior angle in a regular triacontagon is 168? meaning that one exterior angle would be 12?
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| 5. | In other words, 360 " k " ?represents the sum of all the exterior angles.
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| 6. | Equivalently, a convex quadrilateral is cyclic if and only if each exterior angle is equal to the opposite interior angle.
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| 7. | This contradicts Proposition 16 which states that an exterior angle of a triangle is always greater than the opposite interior angles.
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| 8. | However, since the Euclid's exterior angle theorem is a theorem in absolute geometry it is automatically valid in hyperbolic geometry.
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| 9. | The method can be extended to any regular polygon by truncating the catenary at a point corresponding to the exterior angle ."
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| 10. | Exterior angles are quoined with white stone and / white stone " dripstone course " separates the lower and upper half of the building.
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