Question

The ratio between the number of sides of a regular polygon is 2 ∶ 3 and the ratio between their interior angles is 1 ∶ 2. The number of sides of these polygons is respectively
1. 6 and 9
2. 4 and 6
3. 8 and 12
4. 10 and 15

Answer 1

Correct Answer - Option 2 : 4 and 6

Given:

The ratio of the number of sides of two polygons is 2 : 3

And, the ratio between their interior angles is 1 ∶ 2.

Formula used:

Sum of interior angles of a polygon of sides n = (n - 2) × 180°

Calculation:

Let the number of sides of given polygons be 2n and 3n respectively.

Now, ATQ

(2n - 2) × 180°:(3n - 2) × 180° = 1 : 2

⇒ (2n - 2) : (3n - 2) = 1:2

⇒ 4n - 4 = 3n - 2

⇒ 4n - 3n = 4 - 2

⇒ n = 2

⇒ 2n = 4 and 3n = 6

∴ The total number of sides in given polygons is 4 and 6.