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  2. Exterior angle theorem - Wikipedia

    en.wikipedia.org/wiki/Exterior_angle_theorem

    The exterior angle theorem is not valid in spherical geometry nor in the related elliptical geometry. Consider a spherical triangle one of whose vertices is the North Pole and the other two lie on the equator. The sides of the triangle emanating from the North Pole (great circles of the sphere) both meet the equator at right angles, so this ...

  3. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]

  4. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264

  5. Sum of angles of a triangle - Wikipedia

    en.wikipedia.org/wiki/Sum_of_angles_of_a_triangle

    Exterior angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the sum of all three exterior angles, that equals to 360° [9] in the Euclidean case (as for any convex polygon), is less than 360° in the spherical case, and is greater than 360° in the hyperbolic case.

  6. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    Equivalently, a convex quadrilateral is cyclic if and only if each exterior angle is equal to the opposite interior angle. In 1836 Duncan Gregory generalized this result as follows: Given any convex cyclic 2 n -gon, then the two sums of alternate interior angles are each equal to ( n -1) π {\displaystyle \pi } . [ 4 ]

  7. Tangential quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Tangential_quadrilateral

    In a tangential quadrilateral, the four angle bisectors meet at the center of the incircle. Conversely, a convex quadrilateral in which the four angle bisectors meet at a point must be tangential and the common point is the incenter.

  8. Polygon - Wikipedia

    en.wikipedia.org/wiki/Polygon

    Exterior angle – The exterior angle is the supplementary angle to the interior angle. Tracing around a convex n -gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full turn , so the sum of the exterior angles must be 360°.

  9. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In Euclidean geometry, the sum of the exterior angles of a simple convex polygon, if only one of the two exterior angles is assumed at each vertex, will be one full turn (360°). The exterior angle here could be called a supplementary exterior angle. Exterior angles are commonly used in Logo Turtle programs when drawing regular polygons.