ICSE-VIII-Mathematics
16: Understanding Shapes (Including Polygons) Class 8 Maths
- #4-i170° (ii) 138° (ii) 138° (ii) 138° (ii) 138°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˚. (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°. (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°. (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°. (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-ii138°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°.