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If the ratio of an external angle and an internal angle of a regular polygon is 1 : 17, then the number of sides of the regular polygon is
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- 20
- 18
- 36
- 12
- 20
Correct Option: C
Given that , the ratio of an external angle and an internal angle = 1 : 17
Let Number of sides of regular polygon = n
According to question,
| = | ||
| Interior angle | 17 |
| ⇒ | ||
| n | = | |
| 17 | ||
| n |
| ⇒ | = | ||
| 2n - 4 | 17 |
⇒ 2n – 4 = 4 × 17
⇒ 2n – 4 = 68
⇒ 2n = 68 + 4 = 72
| ⇒ n = | = 36 | |
| 2 |
