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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4
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  • #10
    The ratio between the exterior angle and the interior angle of a regular polygon is 1: 4. Find the number of sides in the polygon.
    Ans : Let exterior angle be x° & interior angle be 4x°

    ∴ 4x + x = 180˚
    ⇒ 5x = 180˚
    ⇒ x = 36˚
    ∴ Each exterior angle = 36˚
    Let no. sides = n
    ∴ 360˚/n = 36˚
    ⇒ n = 360˚/36
    ⇒ n = 10