The ratio between each interior angle of a regular polygon and each exterior angle of it is 3 : 2. The number of sides in the polygon is:

1. 6

2. 4

3. 8

4. none of these

It is given that the ratio between each interior angle and each exterior angle of a regular polygon is 3 : 2.

Let the common factor be a. Then,

interior angle = 3a and exterior angle = 2a.

Since the sum of an interior angle and an exterior angle is 180°:

⇒ 3a + 2a = 180°

⇒ 5a = 180°

⇒ a = $\dfrac{180°}{5}$

⇒ a = 36°

Therefore:

Interior angle = 3a = 3 x 36° = 108°

Exterior angle = 2a = 2 x 36° = 72°

According to the properties of a polygon, if a polygon has n sides, each of its exterior angles is $\dfrac{360°}{n}$.

⇒ $\dfrac{360°}{n}$ = 72°

By cross multiplying, we get

⇒ 360° = 72°n

⇒ n = $\dfrac{360°}{72°}$

⇒ n = 5

Hence, option 4 is the correct option.