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What is the relationship between the measure of a central
angle of a polygon and the measures of an interior
and an exterior angle of the polygon?

  • geometry -

    It is important to specify that the following calculations apply to a regular polygon, of which all sides are equal in length, and all interior angles are equal.

    Denote the number of sides by n.

    The total of the central angles make up 360°, so each central angle is 360/n°.

    The exterior angle equals also 360/n°. Note that the exterior angle is the supplement of the interior angle, namely 180° - interior angle.

    The interior angle is therefore 180-exterior angle, and in terms of n, it is
    interior angle = 180 - 360/n

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