This is General approach. If there is a Graph G which have some edges and if we want to find out the complement of the graph then we will take those edges in complimented graph which are not in Graph G.
Number of Edges in Graph G + number of edges in Graph G'= Maximum Edges possible with given vertices.
Cycle graph is a graph which has n vertices and n edges.
In this Question, they are saying," A cycle on n vertices is isomorphic to its complement"
so the number of edges in Graph G and its complimented Graph is same. Let us suppose, n edges are there.
So according to our formula:
n + n =n(n-1)/2
on solving we get