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  2. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n – 2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...

  3. Pentagon - Wikipedia

    en.wikipedia.org/wiki/Pentagon

    For the pentagon, this results in a polygon whose angles are all (360 − 108) / 2 = 126°. To find the number of sides this polygon has, the result is 360 / (180 − 126) = 6 2 ⁄ 3, which is not a whole number. Therefore, a pentagon cannot appear in any tiling made by regular polygons.

  4. 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°.

  5. Table of polyhedron dihedral angles - Wikipedia

    en.wikipedia.org/wiki/Table_of_polyhedron...

    exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex) Tetrahedron {3,3} ... ⁠ 5 / 3 ⁠.6)

  6. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) π radians, or (n − 2)180 degrees, (n − 2)2 right angles, or (n − 2) ⁠ 1 / 2 ⁠ turn. The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles ...

  7. Icositetragon - Wikipedia

    en.wikipedia.org/wiki/Icositetragon

    One interior angle in a regular icositetragon is 165°, meaning that one exterior angle would be 15°.. The area of a regular icositetragon is: (with t = edge length) = ⁡ = (+ + +).

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