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