Question

Find the number of sides in a regular polygon, when each interior angle is: 140°

Answer 1

Each interior angle of a regular polygon

= `(("n" - 2) xx 180°)/"n"`

⇒ `(("n" - 2) xx 180°)/"n"` = 140°

⇒ 180°(n - 2) = 140°(n)
⇒ 9(n - 2) = 7n

⇒ n = `(18)/(2)`
= 9.