Question

Calculate the number of sides of a regular polygon whose interior angles are each 150

Answer 1

Solution :-

The measure in degrees of an interior angle of a regular polygon is given by 180*(n - 2)/n.

Given that the measure of each interior angle of a regular polygon is 150°.

So, we can say that -

180*(n - 2)/n = 150

⇒ (180n - 360)/n = 150

⇒ 180n - 360 = 150n

⇒ 180n - 150n = 360

⇒ 30n = 360

⇒ n = 360/30

⇒ n = 12 

So, the given regular polygon has 12 sides.

Answer 2

Answer

A = 180(n-2)/n

150 = 180(n-2)/n

150n = 180n - 360

360 = 30n

n = 12