Question

Does any polygon have the sum of its angles equal to 1000°? How about 900°?

Answer 1

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

For the sum of the angles of a polygon to be 1000°, we must have:

(n −2) × 180° = 1000°

⇒ n −2 =

⇒ n −2 = 5.555…

⇒ n is not a natural number.

Thus, there is no polygon whose sum of all its angles is 1000°.

For the sum of the angles of a polygon to be 900°, we must have:

(n −2) × 180° = 900°

⇒ n −2 =

⇒ n −2 = 5

⇒ n = 7

Thus, a polygon with seven sides has the sum of its angles as 900°.