Question

Is it possible to have a polygon whose sum of interior angles is 780°?

Answer 1

Let the number of sides in the polygon be n.
∴ (n - 2) x 180° = 780°
⇒ 180°n - 360° = 780°
⇒ 180°n = 1140°

⇒ n = `(1140°)/(180°)`

= `6(1)/(3)`

Since the number of sides of a polygon cannot be in a fraction, therefore the polygon is not possible.