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    If each interior angle of a regular polygon measures 108°, that polygon has _________ sides.
    Question

    If each interior angle of a regular polygon measures 108°, that polygon has _________ sides.

    A.

    6

    B.

    5

    C.

    4

    D.

    10

    Correct option is B

    Given:

    each interior angle=  108°

    Concept Used:

    Interior Angle=(n2)×180n\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} 

    ​where n is the number of sides.

    Solution:

    Given that the interior angle is 108°,  substitute it in formula:

    108=(n2)×180n108 = \frac{(n-2) \times 180}{n} 

    108n=(n2)×180108n = (n-2) \times 180​​

    108n=180n360108n = 180n - 360 

    180n108n=360180n - 108n = 360 

    72n=36072n = 360 

    n=36072=5n = \frac{360}{72} = 5 

    Thus, the polygon has 5 sides.

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