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Maths

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In a regular polygon,each interior angle doubles its corresponding exterior angle,find the number of side of the polygon?

  • Maths -

    let the exterior angle be
    a , b, c , d, e ....
    then the interior angles are
    2a , 2b, 2c, ...

    we know a+b+c+.. = 360

    suppose we have n sides
    sum of interior angles = 180(n-2)

    so 2a + 2b + 2c + ... = 180(n-2)
    2(a+b+c+.. = 180(n-2)
    but a+b+c+..=360
    2(360) = 180(n-2)
    4 = n-2
    n = 6

    There are 6 sides

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