The sum of interior angles of a regular polygon is 3690 . Find the number of sides of the regular poly?

To find the number of sides of the regular polygon, we can use the formula for the sum of interior angles of a polygon:

Sum of interior angles = (n-2) * 180

Where n is the number of sides of the polygon.

Given that the sum of interior angles is 3690, we can set up the equation:

3690 = (n-2) * 180

Solving for n:

3690 = 180n - 360
4050 = 180n
n = 4050 / 180
n = 22.5

Since the number of sides of a polygon must be a whole number, we can conclude that the regular polygon has 22 sides.