Question

A regular polygon has n side and each interior angles =162 find the value of n​

Answer 1

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➡️ 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

Answer 2

Answer:

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

162º.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