HomeLearn Fast select Course
Show Unit/ChapterChange UnitChange SubjectLast Menu
ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4
Qstn# B-2-i Prvs-QstnNext-Qstn
  • #2-i
    160° (ii) 135° (iii) 1 1/5 of a right-angle
    Ans : Let no. of sides of regular polygon be n.
    Each interior angle = 160˚
    ∴ (n - 2)/n × 180˚ = 360˚
    ⇒ 180˚n - 360˚ = 160n
    ⇒ 20n = 360˚
    ⇒ n = 18 (ii) No. of sides = n
    Each interior angle = 135˚
    (n - 2)/n × 180˚ = 135˚
    ⇒ 180n - 360˚ = 135n
    ⇒ 180n - 135n = 360˚
    ⇒ 45n = 360˚
    ⇒ n = 8 (iii) No. of sides = n
    Each interior angle = 1 1/5 right angles
    = 6/5 × 90˚
    = 108˚
    ∴ (n - 2)/n × 180˚ = 108˚
    ⇒ 180n - 360 ˚ = 108n
    ⇒ 180n -108n = 360˚
    ⇒ 72n = 360˚
    ⇒ n = 5
  • #2-ii
    135°
    Ans : No. of sides = n
    Each interior angle = 135˚
    (n - 2)/n × 180˚ = 135˚
    ⇒ 180n - 360˚ = 135n
    ⇒ 180n - 135n = 360˚
    ⇒ 45n = 360˚
    ⇒ n = 8
  • #2-iii
    1 1/5 of a right-angle
    Ans : No. of sides = n
    Each interior angle = 1 1/5 right angles
    = 6/5 × 90˚
    = 108˚
    ∴ (n - 2)/n × 180˚ = 108˚
    ⇒ 180n - 360 ˚ = 108n
    ⇒ 180n -108n = 360˚
    ⇒ 72n = 360˚
    ⇒ n = 5