Question

14. An exterior angle and the interior angle of a regular polygon are in the ratio 2 : 3 respectively. Find the
number of sides that the polygon has.
​

Answer 1

⛦ Given :

• Ratio of exterior angle and interior angle of the polygon is 2 : 3.

⛦ To find :

• The number of the sides a polygon have.

⛦ Solution :

As it is given that the exterior angle and the interior angle are in ratio 2:3

So, let's assume the exterior angle as 2x

And, Interior angles as 3x

Thus,

According to Question,

⟼ 2x + 3x = 180°

⟼ 5x = 180°

⟼ x = 180°/5

⟼ x = 36°

∴ Exterior angle (2x) = 2×36 = 72°

And Interior angle (3x) = 3×36 = 108°

• Each side of the polygon = 360/no. of exterior angle

• Each side of the polygon = 360/72

• Each side of the polygon = 5

Thus, Number of side in polygon is 5.