Is the sum of the angles of any polygon 1600°? How about 900°?

Given: Sum of the angles = 1600° and 900°

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

⇒ 1600° = (n – 2) × 180°

⇒

⇒ 8.89 = n – 2

⇒ n = 8.89 + 2

⇒ n = 10.89

∴ There is no polygon which have sum of the angles as 1600°.

When sum is 900°

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

⇒ 900° = (n – 2) × 180°

⇒

⇒ 5 = n – 2

⇒ n = 5 + 2

⇒ n = 7

∴ The number of sides of polygon having sum of the angles of 900° is 7 sides.