prove that the exterior angle of polygon is 360

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  1. From the centre of a polygon of n-sides (n-gon), draw rays towards the n-vertices thus forming n triangles.

    The sum of internal angles of the n triangles equals 180n°. This sum also equals the sum of the n interior angles plus the angles around the central point, 360°. Call this sum A.

    Extend each side of the n-gon to create an exterior angle. The sum of the exterior angle and the corresponding interior angle equals 180°. So the sum of all the exterior angles and interior angles of the n-gon equals 180n°. Call this sum B.

    Since both equal 180n°,
    sum A = sum B, or
    360°+∑interior angles = ∑exterior angles + ∑ interior angles
    Cancel out ∑interior angles, we get
    ∑exterior angles = 360°.

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