Geometry is fun

Discussion in 'Pseudoscience' started by BdS, May 13, 2016.

  1. BdS Registered Senior Member

    Messages:
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    The formula for interior angles of a polygon is: 180 x (number of sides - 2) <- http://www.math-prof.com/Geom/Geom_Ch_30.asp

    If the interior (INT) angles of a triangle a, b, c is equal to 180⁰ then the exterior (EXT) angles equal to 900⁰.


    a_full_angle = 360⁰
    b_full_angle = 360⁰
    c_full_angle = 360⁰
    a_full_angle + b_full_angle + c_full_angle = 1080⁰
    full_angle_total = 1080⁰

    a_INT = 40⁰
    b_INT = 60⁰
    c_INT = 80⁰
    a_INT + b_INT + c_INT = 180⁰
    triangle_INT_total = 180⁰

    a_EXT = 320⁰
    b_EXT = 300⁰
    c_EXT = 280⁰
    a_EXT + b_EXT + c_EXT = 900⁰
    triangle_EXT_total = 900⁰

    a_full_angle = 360⁰ = a_INT + a_EXT
    b_full_angle = 360⁰ = b_INT + b_EXT
    c_full_angle = 360⁰ = c_INT + c_EXT
    full_angle_total = 1080⁰ = triangle_INT_total + triangle_EXT_total

    If the interior angles of a Quadrilateral (four sided polygon) equal 360⁰ then the exterior angles equal:
    360⁰ x 4 = 1440⁰
    1440⁰ – 360⁰ = 1080⁰

    If the interior angles of a Pentagon (five sided polygon) equal 540⁰ then the exterior angles equal:
    360⁰ x 5 = 1800⁰
    1800⁰ – 540⁰ = 1260⁰

    If the interior angles of a Hexagon (six sided polygon) equal 720⁰ then the exterior angles equal:
    360⁰ x 6 = 2160⁰
    2160⁰ – 720⁰ = 1440⁰


    If the interior angles of a Heptagon (seven sided polygon) equal 900⁰ then the exterior angles equal:
    360⁰ x 7 = 2520⁰
    2520⁰ – 900⁰ = 1620⁰

    If the interior angles of an Octagon (eight sided polygon) equal 1080⁰ then the exterior angles equal:
    360⁰ x 8 = 2880⁰
    2880⁰ – 1080⁰ = 1800⁰

    Etc...

    Is the formula for the exterior angles of a polygon?

    n = number of sides of the polygon

    (360 x n) – (180 x (n - 2))

    Is there a better way to do this?
     

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