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13 March, 15:30

In a certain regular polygon, the measure of each interior angle is four times the measure of each exterior angle. Find the number of sides in this regular polygon.

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  1. 13 March, 15:31
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    Answer: 10

    Step-by-step explanation:

    Let x be the measure of each exterior angle (in degrees).

    Then the measure of each interior angle (in degrees) = 4x

    We know that the sum of exterior angle and interior angle = 180 degrees.

    i. e. x+4x = 180

    i. e. 5x = 180

    i. e. x = 36 [Divide both sides by 5]

    i. e. The measure of each exterior angle = 36°

    Also, Sum all exterior angles is 360°.

    Number of sides in regular polygon = 360° : (Measure of each exterior angle)

    = 360° : 36

    =10

    Therefore, the number of sides in this regular polygon = 10
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