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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 2
Qstn# A-6 Prvs-QstnNext-Qstn
  • #6
    Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with : (i) 7 sides (ii) 10 sides (iii) 250 sides. (i) 7 sides (ii) 10 sides (iii) 250 sides.
    Ans : (i) No. of sides n = 7
    Sum of interior & exterior angles at one vertex = 180°
    Sum of interior & exterior angles = 7 × 180˚
    = 1260Ëš
    Sum of interior angles = (n - 2) × 180˚
    = (7 - 2) × 180˚
    = 900Ëš
    ∴ Sum of exterior angles = 1260˚ - 900˚
    = 360Ëš (ii) No. of sides n = 10
    Sum of interior and exterior angles = 10 × 180˚
    = 1800Ëš
    But sum of interior angles = (n - 2) × 180˚
    = (10 - 2) × 180˚
    = 1440Ëš
    ∴ Sum of exterior angles = 1800 - 1440
    = 360Ëš (iii) No. of sides n = 250
    Sum of all interior and exterior angles = 250 × 180˚
    = 45000Ëš
    But sum of interior angles = (n - 2) × 180˚
    = (250 - 2) × 180˚
    = 248 × 180˚
    = 44640Ëš
    ∴ Sum of exterior angles = 45000 - 44640
    = 360Ëš (i) No. of sides n = 7
    Sum of interior & exterior angles at one vertex = 180°
    Sum of interior & exterior angles = 7 × 180˚
    = 1260Ëš
    Sum of interior angles = (n - 2) × 180˚
    = (7 - 2) × 180˚
    = 900Ëš
    ∴ Sum of exterior angles = 1260˚ - 900˚
    = 360Ëš (ii) No. of sides n = 10
    Sum of interior and exterior angles = 10 × 180˚
    = 1800Ëš
    But sum of interior angles = (n - 2) × 180˚
    = (10 - 2) × 180˚
    = 1440Ëš
    ∴ Sum of exterior angles = 1800 - 1440
    = 360Ëš (iii) No. of sides n = 250
    Sum of all interior and exterior angles = 250 × 180˚
    = 45000Ëš
    But sum of interior angles = (n - 2) × 180˚
    = (250 - 2) × 180˚
    = 248 × 180˚
    = 44640Ëš
    ∴ Sum of exterior angles = 45000 - 44640
    = 360Ëš
  • #6-i
    7 sides
    Ans : No. of sides n = 7
    Sum of interior & exterior angles at one vertex = 180°
    Sum of interior & exterior angles = 7 × 180˚
    = 1260Ëš
    Sum of interior angles = (n - 2) × 180˚
    = (7 - 2) × 180˚
    = 900Ëš
    ∴ Sum of exterior angles = 1260˚ - 900˚
    = 360Ëš
  • #6-ii
    10 sides
    Ans : No. of sides n = 10
    Sum of interior and exterior angles = 10 × 180˚
    = 1800Ëš
    But sum of interior angles = (n - 2) × 180˚
    = (10 - 2) × 180˚
    = 1440Ëš
    ∴ Sum of exterior angles = 1800 - 1440
    = 360Ëš
  • #6-iii
    250 sides.
    Ans : No. of sides n = 250
    Sum of all interior and exterior angles = 250 × 180˚
    = 45000Ëš
    But sum of interior angles = (n - 2) × 180˚
    = (250 - 2) × 180˚
    = 248 × 180˚
    = 44640Ëš
    ∴ Sum of exterior angles = 45000 - 44640
    = 360Ëš