Question

If each interior angle of a regular polygon is 144⁰,then the number of sides of the polygon is

8

9

10

12​

Answer 1

If each interior angle of a regular polygon is 144° then the number of sides of the polygon is 10

Answer 2

Concept:

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular and equilateral.

Given:

We are given that the interior angle of a regular polygon is 144⁰.

Find:

We need to find the number of sides of the polygon.

Solution:

First, we can calculate the exterior angle of the polygon:

Exterior angle=180°-interior angle

E=180°-144°

E=36°

Now, we know that the sum of the exterior angles of a regular polygon is 360°.

So, let the number of sides of the polygon be x.

x=360°÷36°

x=10

Therefore, the number of sides of the polygon with interior angle as 144° are 10 sides.

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