The sum of the 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?

Given: Sum of the angles = 1980°

Sum of the angles of n-sided polygon = (n – 2) × 180°

⇒ 1980° = (n – 2) × 180°

⇒

⇒ 11 = n – 2

⇒ n = 11 + 2

⇒ n = 13

∴ The number of sides of polygon having sum of the angles of 1980° is 13 sides.

When the number of sides of polygon one side less than 13-sided polygon.

Number of sides of polygon = 12

Sum of the angles of n-sided polygon = (n – 2) × 180°

⇒ S = (12 – 2) × 180°

⇒ S = 10 × 180°

⇒ S = 1800

∴ The sum of the angles of 12-sided polygon is 1800°.

When the number of sides of polygon one side more than 13-sided polygon.

Number of sides of polygon = 14

Sum of the angles of n-sided polygon = (n – 2) × 180°

⇒ S = (14 – 2) × 180°

⇒ S = 12 × 180°

⇒ S = 2160

∴ The sum of the angles of 14-sided polygon is 2160°.