A polygon of n sides has number of diagonals ‌=‌
n(n−3)
2
=275‌‌‌ (given) ‌ ‌⇒‌‌n2−3n−550=0 ‌⇒‌‌n2−25n+22n−550=0 ‌⇒‌‌n(n−25)+22(n−25)=0 ‌⇒‌‌(n−25)(n+22)=0 ‌⇒‌‌n=25,(∵n=−22‌ is not possible ‌) ‌