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The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively
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- 6, 12
- 5, 10
- 4, 8
- 7, 14
- 6, 12
Correct Option: C
We know that ,
| Each interior angle = | |
| n |
According to question ,
| n | = | |
| 3 | ||
| 2n |
[∵ Ratio of number of sides is 1 : 2]
| ⇒ | = | ||
| 4n - 4 | 3 |
| ⇒ | = | ||
| 4n - 4 | 3 |
⇒ 6n – 12 = 4n – 4
⇒ 6n – 4n = 12 – 4 = 8
⇒ 2n = 8 ⇒ n = 4
∴ No. of sides = 4, 8
