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15 January, 06:00

If the measure of one interior angle of a regular polygon is 156 degrees, how many sides does it have? Can a regular polygon have and interior angle of 157 degrees? Explain your answer

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  1. 15 January, 07:07
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    One exterior angle = 180 - 156 = 24 degrees

    Recall that the sum of all the exterior angles of a polygon add up to 360 degrees.

    So the number of sides in this polygon = number of exterior angles = 360 / 24

    = 15

    If interior angles was 157, exterior one = 23 degrees

    360 / 23 does not divide to give an integer

    so a regular polygon cannot have an interior angle of 157.
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