Question

The internal angles of a plane polygon are in AP. The smallest angle is 100° and the common difference is 10°. Find the number of sides of the polygon.  

Answer 1

Smallest interior angle = 100, largest exterior angle= 180 − 100 =80

Similarly other exterior angles are 70, 60, 50, …. 

Sum of all the exterior angles = 360

So n(2.80 +(n-1)(-10))/2 =   360 or n(17 − n) = 72

We can see that the above equation is true for both n = 8, 9. But for n = 9, the 9^th exterior angle must be 0 which is not possible so only 8 is possible.