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

Given,

Ratio between an exterior angle and an interior angle of a regular polygon is 2 : 3.

Let exterior angle be 2x and interior angle be 3x.

We know that,

At each vertex of every polygon,

⇒ Exterior angle + Interior angle = 180°

⇒ 2x + 3x = 180°

⇒ 5x = 180°

⇒ x = $\dfrac{180°}{5}$ = 36°.

⇒ 2x = 2 × 36° = 72°, 3x = 3 × 36° = 108°.

By formula,

If each exterior angle of a regular polygon is x°, the number of sides in it = $\dfrac{360°}{x°}$

No. of sides in a regular polygon with exterior angle = 72° is $\dfrac{360°}{72°}$ = 5.

Hence, no. of sides in polygon = 5.