The difference between any two consecutive interior angles of a polygon is 5°.

It’s understood from the question that, the angles of the polygon will form an A.P. with common difference d = 5° and first term a = 120°.

And, we know that the sum of all angles of a polygon with n sides is 180° (n – 2).

Thus, we can say

s_n = 180° (n – 2)

\( s_n=\dfrac{n}{2}[2a+(n-1)d]\)

= 180° (n – 2)

\(=\dfrac{n}{2}[240°+(n-1)5°]\)

= 180° (n – 2)

= n[240+5n−5]=360(n−2)

= 240n+5n²−5n=360n−720

= 5n²−125n+720=0

= n²−25n+144=0

= (n−9)(n−16)=0

n = 9,16

Therefore, the number of the sides of the polygon 9 or 16 .