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Two regular polygons are such that the ratio between their number of sides is 1 : 2 and the ratio of measures of their interior angles is 3 : 4. Then the number of sides of each polygon is
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- 10 and 20
- 4 and 8
- 3 and 6
- 5 and 10
- 10 and 20
Correct Option: D
Given , The ratio between their number of sides = 1 : 2
and the ratio of measures of their interior angles = 3 : 4.
As we know that ,
| Each interior angle of n –sided polygon = | right angles | |
| n |
According to the question,
| y | = | |
| 4 | ||
| 2y |
| ⇒ | × | = | |||
| y | 4y - 4 | 4 |
| = | = 3 | |
| y - 1 |
⇒ 4y – 8 = 3y – 3
⇒ 4y – 3y = 8 – 3
⇒ y = 5
∴ Number of sides of polygons = 5 and 10.
