The interior angles of a polygon are in A.P. If the smallest angle is 100° and the common difference is 4°, then the number of sides is

Explanation:

The interior angles of a polygon are in A.P.

The smallest angle =100°

Common difference =4°

= 100,104,108,⋯⋯n

Sum of interior angles of n−sided polygon

= (n−2)180°=n2[2a+(n−1)d]

= (n−2)360=n[200+(n−1)4]

= 360n−720=n[4n+196]

= 360n−720=4n2+196n

= 4n²−164n+720=0

= n2−41n+180=0

= (n−36)(n−5)=0

= n=36 or n=5

n=36>180°(concave)

n=5