Question

the sum of angles of a polygon is 1980°.What is the sum of the angles of a polygon with one side less? What about a polygon with one side more?

Answer 1

The formula for sum of interior angles is S = (n - 2) * 180.

Therefore, 1980° = (n - 2) * 180.

or, (n - 2) = 1980 / 180 = 11.

or, n = 13.

Therefore there are 13 sides in total.

each angle will be 1980/13.

With one side less it will be (1980 * 12) / 13. = 1827.69°

With one side more it will be (1980 * 14) / 13. = 2132.30°