Question

If each interior angle of a regular polygon is 162°
, then the number of sides in it is
a. 20 b. 10 c.6 d.8

Answer 1

Answer:

c. 6 is your correct answer

Answer 2

Answer:

A)20

Step-by-step explanation:

Sum of all the interior angles of any convex polygon of 'n' sides is (2n-4)*90°…(1)

Given that the polygon is regular polygon.we know that regular polygon has all sides equal in length and all angles equal in length and given that each angle is 162° .So sum of n angles is n*162 …(2)

Equating (1)&(2),

(2n-4)*90=n*162

180n-360=162n

18n=360

n=360/18=20

Hence the number of sides of given regular polygon each of interior angle 162° is 20

hope it helps :)