Find the number of sides of a regular polygon if one interior angle is 60 degrees.

Solution:

Given, one interior angle is 60 degrees.

We have to find the number of sides of a regular polygon.

We know, Sum of interior angles of a regular polygon = (n - 2) × 180°

So, Interior angle of a regular polygon = [(n - 2)×180°]/n

60 = [(n - 2) × 180°]/n

60n = [(n - 2) × 180°]

60n = 180n - 360

On rearranging,

180n - 60n = 360

120n = 360

12n = 36

n = 36/12

n = 3

Therefore, the number of sides is 3.

Find the number of sides of a regular polygon if one interior angle is 60 degrees.

Summary:

The number of sides of a regular polygon if one interior angle is 60 degrees is 3 and it is an equilateral triangle.