Question

If one of the interior angles of a regular polygon is found to be 9 / 8 times of one of the interior angles of a regular hexagon, then the number of sides of the polygon is?
1. 12
2. 10
3. 14
4. 8

Answer 1

Correct Answer - Option 4 : 8

Concept used:

One interior angle of a regular polygon = (n - 2)180º/n

Calculation:

One of the internal angle of a regular hexagon = (4 × 180º)/6 = 120º

⇒ (n - 2)180º/n = \(\frac{9}{8} \) × 120º

⇒ (n - 2)/n = \(\frac{9}{8} \) × \(\frac{2}{3}\)

⇒ (n - 2)/n = 3/4

⇒ 4n - 8 = 3n

⇒ n = 8

∴ The number of sides of the polygon is 8.