Question

The external angle of a regular polygon is between 18 and 24 if it has a integral value then the sum of angles of polygon is​

Answer 1

Answer:

Let there be an n sided polygon.

It is known that the sum of the interior angles of an n sided polygon is

S=(n−2)×180o. 

S will have least positive integral value, which is >0

(n−2)=1⟹n=3. 

∴  It is a triangle. 

But it is a regular polygon, so the triangle is equiangular.

i.e One interior angle is 60o

This is the least measure of an interior triangle of a regular polygon. ∴ Here the exterior angle will be the greatest, since the interior and exterior angles are supplimentery to each other. 

i.e The greatest exterior angle is 180o−60o=120o

Hence, the answer is 120o.