Question

The sum of the angles of a polygon is 2160°. What is the sum of the angles of a polygon with one more side? What about a polygon with one side less?

Answer 1

Sum of angles of the given polygon = 2160°

We know that the sum of the angles of polygon with n sides = (n −2) × 180°

⇒ (n −2) × 180° = 2160°

⇒ n −2 =

⇒ n −2 = 12

⇒ n = 14

∴Number of sides in the given polygon = 14

Number of sides in the second polygon = 14 + 1 = 15

Sum of the angles of the second polygon = (n −2) × 180°

= (15 − 2) × 180°

= 13 × 180°

= 2340°

Thus, sum of the angles of a polygon with 15 sides is 2340°.

Number of sides in the third polygon = 14 − 1 = 13

Sum of the angles of the third polygon = (n −2) × 180°

= (13 − 2) × 180°

= 11 × 180°

= 1980°

Thus, the sum of the angles of a polygon with 13 sides is 1980°.