Number of diagonals in polygon =54 Let the number of sides in polygon =n Then, The number of diagonal in any polygon =‌
n(n−3)
2
54=‌
n(n−3)
2
n2−3n=108 n2−3n−108=0 n2−12n+9n−108=0 n(n−12)+9(n−12)=0 (n+9)(n−12)=0 n=−9‌ or ‌n=12 ‌ (not possible ‌) Hence, the number of sides in polygon is n=12