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If the ratio of numer of sides of two regular polygons be 2 : 3 and the ratio of their interior angles be 6 : 7, find the number of sides of the two polygons.
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- 6 and 7
- 8 and 9
- 6 and 9
- 6 and 8
- 6 and 7
Correct Option: C
Given that , The ratio of number of sides of two regular polygons = 2 : 3
and the ratio of interior angles of two regular polygons = 6 : 7
| Each interior angle of a regular polygon of n sides = |  |  | right angles | |
| n |
Let the number of sides be 2y and 3y respectively.
According to question ,
| ∴ | ||
| 2y | = | |
| 7 | ||
| 3y |
| ⇒ | = | ||
| 2(6y - 4) | 7 |
| ⇒ | = | ||
| 12y - 8 | 7 |
| ⇒ | = | ||
| 3y - 2 | 7 |
⇒ 7y – 7 = 6y – 4
⇒ y = 7 – 4 = 3
∴ Number of sides = 2y = 2 × 3 = 6 and 3y = 3 × 3 = 9.
