If the difference between the exterior and the interior angles of a regular polygon is 60^o, with an interior angle being greater than the corresponding exterior angle, then find the number of sides of the polygon.

Correct option is C

Given:

Difference between interior angle and exterior angle = 60^∘

Interior angle is greater than the exterior angle

We are to find the number of sides of the regular polygon

Concept Used:
For a regular polygon with n sides:

Exterior angle = $$\frac{360^\circ}{n}$$​​

Interior angle = $$180^\circ - \frac{360^\circ}{n}$$​​

Solution:

From the given condition;

​$$(180^\circ - \frac{360^\circ}{n}) - \frac{360^\circ}{n} = 60^\circ$$​​

​$$180^\circ - \frac{720^\circ}{n} = 60^\circ$$​​

​$$\frac{720^\circ}{n} = 120^\circ$$​​

​$$n = \frac{720}{120} = 6$$​​