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The sum of the interior angles of a poly...

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.

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Given: The sum of the interior angles of a polygon is three times the sum of its exterior angles.
Sum of all interior angles of a regular polygon`=180^@(n−2)`, where `n` is number of sides of a polygon
Sum of all exterior angle of a regular polygon`=360^@`
According to question,`180^@(n−2)=3xx360^@`
`=>(n−2)=6`
`=>n=8`
Hence, the number of sides of the polygon is `8`.
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Knowledge Check

  • Each interior angle of a regular polygon is three times its exterior angle, then the number of sides of the regular polygon is :

    A
    9
    B
    8
    C
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  • The sum of all the interior angles of a regular polygon is four times the sum of its exterior angles. The polygon is :

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    B
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    D
    nonagon

  • The sum of all the interior angles of a regular polygon is four times the sum of its exterior angles. The polygon is:

    A
    hexagon
    B
    triangle
    C
    decagon
    D
    nonagon

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