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maths

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each interior angle of a regular polygon is 18 degree more than eight times an exterior angle. the number os sides of polygon is.

  • maths -

    at each vertex, interior + exterior = 180 degrees.

    If exterior = x,

    x+(8x+18) = 180
    9x = 162
    x = 18

    he exterior angle of a regular n-gon is 360/n, so

    18 = 360/n
    n = 20

  • maths -

    Interior angle = 180 - (exterior angle) = 180 -360/N

    Exterior angle = 360/N

    180 - (360/N) = [8*360/N] +18
    9*360/N = 162
    N = 20 sides

    It is called an icosagon

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