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21 June, 17:21

what is the ratio of the number of degrees in the interior angle of a regular pentagon to the number of degrees in the interior angle of a regular hexagon? express your answer as a common fraction.

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  1. 21 June, 17:32
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    Answer: Answer is 3/4

    Step-by-step explanation: The sum of the interior angles of a regular polygon is calculated as follows;

    (n-2) * 180° {where n represents the number of sides of the polygon}

    A pentagon is a polygon with five equal sides. Therefore the sum of it's interior angles is calculated as;

    (5-2) * 180°

    =3*180°

    =540°

    A hexagon is a polygon with six equal sides. Therefore the sum of it's interior angles is calculated as;

    (6-2) * 180°

    =4*180°

    =720°

    Therefore, the ratio of the number of degrees in the interior angles of a regular pentagon, to the number of degrees in the interior angles of a regular hexagon is given as

    540:720

    If you divide both sides by their prime factors (2*2*3*3*5) the ratio becomes

    3:4 in it's simplest form.

    As a common fraction, it can be expressed as

    3/4.
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