Question

Each interior angle of a 2n-sided regular

polygon is 162°. Find the interior angle of

another polygon with 3n-side.​

Answer 1

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