Question

18) Find the number of sides of a regulare polygon, when
each of its angles has a mesaure of
(i)166°
(ii)179°​

Answer 1

Answer:-

(i) Each interior angle of a regular polygon = 180°(n*2)/n where n = number of sides of polygon.

Given, each of its angles has a measure of 166°

180°(n-2)/n = 166°

⇒180°n-166°n = 360°

⇒14°n = 360°

⇒n = 360/14

⇒n = 9

(ii) Each interior angle of a regular polygon = 180°(n-2)/n where n = number of sides of polygon.

Given, each of its angles have a measure of 179°

180°(n-2)/n = 179°

⇒180°n - 179°n = 360°

⇒1°n = 360°

⇒n = 360/1

⇒n = 360°