Question

Is it possible to have a polygon, whose sum of interior angles is 1030°.

Answer 1

Let no. of. sides be = n

Sum of interior angles of polygon = 1030°

∴ (2n - 4) × 90° = 1030°

⇒ 2(n - 2) = `(1030°)/(90°)`

⇒ (n - 2) = `(1030°)/(2 xx 90°)`

⇒ (n - 2) = `103/18`

⇒ n = `103/18 + 2`

⇒ n = `139/18`

Which is not a whole number. Hence it is not possible to have a polygon, the sum of whose interior angles is 1030°.