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

Correct option is A

Given:

Difference between interior and exterior angles = $$60^\circ$$​​
Interior angle > Exterior angle

Formula Used:
For a regular polygon with n sides:

Interior angle = $$\frac{(n - 2) \times 180^\circ}{n}$$​​

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

Solution:

$$\left( \frac{(n - 2) \times 180}{n} \right) - \left( \frac{360}{n} \right) = 60 \\ \ \\\frac{180n - 360 - 360}{n} = 60\\ \ \\\frac{180n - 720}{n} = 60$$​

180n  - 720 = 60n

120n = 720

n = 6 sides