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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4
Qstn# B-9 Prvs-QstnNext-Qstn
  • #9
    The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find : (i) each exterior angle of the polygon ; (ii) number of sides in the polygon (i) each exterior angle of the polygon ; (ii) number of sides in the polygon
    Ans : Interior angle : exterior angle = 2 : 1
    Let interior angle = 2x° & exterior angle = x°

    ∴ 2x˚ + x˚ = 180˚
    ⇒ 3x = 180˚ (i) x = 60˚
    ∴ Each exterior angle = 60˚
    Let angle of sides = n
    ∴ 360˚/n = 60˚
    ⇒ n = 360˚/60˚
    dlt29025704036958965620">⇒ n = 360˚/60˚ (ii) n = 6
    ∴ (i) 60˚ (ii) 6 (i) x = 60˚
    ∴ Each exterior angle = 60˚
    Let angle of sides = n
    ∴ 360˚/n = 60˚
    ⇒ n = 360˚/60˚
    dlt29025704036958965620">⇒ n = 360˚/60˚ (ii) n = 6
    ∴ (i) 60˚ (ii) 6
  • #9-i
    each exterior angle of the polygon ;
    Ans : x = 60Ëš
    ∴ Each exterior angle = 60˚
    Let angle of sides = n
    ∴ 360˚/n = 60˚
    ⇒ n = 360˚/60˚
    dlt29025704036958965620">⇒ n = 360˚/60˚
  • #9-ii
    number of sides in the polygon
    Ans : n = 6
    ∴ (i) 60˚ (ii) 6