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