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The ratio of each interior angle to each exterior angle of a regular polygon is 3 : 1. The number of sides of the polygon is
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- 9
- 7
- 6
- 8
- 9
Correct Option: D
Let Number of sides of polygon = n
According to the question,
The ratio of each interior angle to each exterior angle of a regular polygon = 3 : 1
| : | = | ||||
| n | n | 1 |
| ⇒ | = | ||
| 360° | 1 |
| ⇒ | = | ||
| 4 | 1 |
⇒ 2n – 4 = 4 × 3 = 12
⇒ 2n = 12 + 4 = 16
| ⇒ n = | = 8 | |
| 2 |
