Question

the external angle of a regular polygon is between 18 and 24 if it has a integral value than the sum of angles of a 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.

Step-by-step explanation:

please follow me

Answer 2

Step-by-step explanation:

The number of values of p for which the polygon will have angles whose ... 24-2=22 regular polygons exist which have interior angles equal to an integer: 3 ... so for angle to be an integer, 360/n should be an integer