Question

Is it possible to have a polygon, whose sum of interior angle is: 870°

Answer 1

Let no. of sides = n

Sum of angles = 870°

(n - 2) × 180° = 870°

n - 2 = `870/180`

n - 2 = `29/6`

n = `29/6 + 2`

n = `29/6 + 2/1`

n = `(29 + 12)/6`

n = `41/6`

Which is not a whole number.

Hence it is not possible to have a polygon, the sum of whose interior angles is 870°.