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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 3
Qstn# B-4 Prvs-QstnNext-Qstn
  • #4
    Is it possible to have a regular polygon whose each interior angle is : (i) 170° (ii) 138° (i) 170° (ii) 138°
    Ans : (i) No. of sides = n
    each interior angle = 170°
    ∴ (n - 2)/n × 180˚ = 170˚
    ⇒ 180n - 360˚ = 170n
    ⇒ 180n - 170n = 360˚
    ⇒ 10n = 360˚
    ⇒ n = 360˚/10˚
    ⇒ n = 36
    which is a whole number.
    Hence it is possible to have a regular polygon whose interior angle is 170˚. (ii) Let no. of sides = n
    Each interior angle = 138˚
    ∴ (n - 2)/n × 180˚ = 138˚
    ⇒ 180n - 360˚ = 138n
    ⇒ 180n - 138n = 360˚
    ⇒ 42n = 360˚
    ⇒ n = 360˚/42
    ⇒ n = 60˚/7
    Which is not a whole number.
    Hence it is not possible to have a regular polygon having interior angle of 138°. (i) No. of sides = n
    each interior angle = 170°
    ∴ (n - 2)/n × 180˚ = 170˚
    ⇒ 180n - 360˚ = 170n
    ⇒ 180n - 170n = 360˚
    ⇒ 10n = 360˚
    ⇒ n = 360˚/10˚
    ⇒ n = 36
    which is a whole number.
    Hence it is possible to have a regular polygon whose interior angle is 170˚. (ii) Let no. of sides = n
    Each interior angle = 138˚
    ∴ (n - 2)/n × 180˚ = 138˚
    ⇒ 180n - 360˚ = 138n
    ⇒ 180n - 138n = 360˚
    ⇒ 42n = 360˚
    ⇒ n = 360˚/42
    ⇒ n = 60˚/7
    Which is not a whole number.
    Hence it is not possible to have a regular polygon having interior angle of 138°.
  • #4-i
    170°
    Ans : No. of sides = n
    each interior angle = 170°
    ∴ (n - 2)/n × 180˚ = 170˚
    ⇒ 180n - 360˚ = 170n
    ⇒ 180n - 170n = 360˚
    ⇒ 10n = 360˚
    ⇒ n = 360˚/10˚
    ⇒ n = 36
    which is a whole number.
    Hence it is possible to have a regular polygon whose interior angle is 170˚.
  • #4-ii
    138°
    Ans : Let no. of sides = n
    Each interior angle = 138˚
    ∴ (n - 2)/n × 180˚ = 138˚
    ⇒ 180n - 360˚ = 138n
    ⇒ 180n - 138n = 360˚
    ⇒ 42n = 360˚
    ⇒ n = 360˚/42
    ⇒ n = 60˚/7
    Which is not a whole number.
    Hence it is not possible to have a regular polygon having interior angle of 138°.