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    ​For a regular polygon. the sum of the interior angles is 200% more than the sum of its exterior angles. Each interior angle of the polygon measures x
    Question

    ​For a regular polygon. the sum of the interior angles is 200% more than the sum of its exterior angles. Each interior angle of the polygon measures x°. What is the value of x°?

    A.

    144°

    B.

    135°

    C.

    140°

    D.

    108°

    Correct option is B

    Given:
    Sum of interior angles is 200% more than sum of exterior angles.

    Formula Used:

    Sum of exterior angles = 360

    Sum of interior angles = (n2)×180(n - 2) \times 180^\circ​​

    Solution:

    Sum of interior angles=3×Sum of exterior angles =3×360=1080\text{Sum of interior angles} = 3 \times \text{Sum of exterior angles}\\ \ \\ = 3 \times 360 = 1080^\circ

    Now, 

    (n2)×180=1080 n2=6 n=8(n - 2) \times 180 = 1080 \\ \ \\ n - 2 = 6 \\ \ \\ n = 8​​

    Each interior angle:

    (n2)×180n=6×1808=135\frac{(n - 2) \times 180}{n} = \frac{6 \times 180}{8} = 135^\circ​​

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