In a regular pentagon the ratio of interior angle : exterior angle =
3 : 2
A pentagon has 5 sides. Since the pentagon is regular, all its angles and sides are equal.
Let the interior angle be x∘ and exterior angle be y∘.
∵ sum of exterior angles in a polygon is 360∘
⇒5y∘ = 360∘
⇒y∘=3605=72∘
∵ sum of exterior angle and its respective interior angle in a polygon is 180∘
⇒x+y=180∘
⇒x=180∘−y∘
=180∘−72∘
=108∘
Now, interior angleexterior angle = xy=10872=32
Hence, interior angle : exterior angle = 3 : 2