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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4
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  • #13
    Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
    Ans :
    Let number of sides of regular polygon = n
    AB & DC when produced meet at P such that
    ∠P = 90˚
    ∵ Interior angles are equal.
    ∴ ∠ABC = ∠BCD
    ∴ 180˚ - ∠ABC = 180˚ - ∠BCD
    ∴ ∠PBC = ∠BCP
    But ∠P = 90˚ (Given)
    ∴ ∠PBC + ∠BCP = 180˚ - 90˚ = 90˚
    ∴ ∠PBC = ∠BCP
    = ½ × 90˚
    = 45Ëš
    ∴ Each exterior angle = 45˚
    ∴ 45˚ = 360˚/n
    ⇒ n = 360˚/45˚
    ⇒ n = 8