The ratio between the number of sides of two regular polygons

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The ratio between the number of sides of two regular polygons

Home » Aptitude » Plane Geometry » Question

The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively

1. 6, 12
2. 5, 10
3. 4, 8
4. 7, 14

Correct Option: C

We know that ,
Each interior angle = (2n - 4) × 90°
n

According to question ,
(2n - 4) × 90°
n = 2
(4n - 4) × 90° 3
2n

[∵ Ratio of number of sides is 1 : 2]
⇒ (2n - 4) × 2 = 2
4n - 4 3

⇒ 2n - 4 = 1
4n - 4 3

⇒ 6n – 12 = 4n – 4
⇒ 6n – 4n = 12 – 4 = 8
⇒ 2n = 8 ⇒ n = 4
∴ No. of sides = 4, 8