Let's take one vertex. It can be linked to 7 other vertices.
Let's take the next vertex. It can also be linked to 7 other vertices but there is one diagonal that is already drawn. Therefore, there is 6 new diagonals.
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Originally Posted by Carrick
The above quote is from a PM: please ask such questions in the open. Others may also benefit from the answer.
An octagon is a figure with eight vertices and eight edges. If two edges share a vertex, then the edges are said to be adjacent. But any two vertices will determine a line segment. If you join each vertex with each other vertex we have what is known as a complete graph. In the case of eight vertices the complete graph, , has 28 edges. The diagonals are the edges that are in the original octagon. Thus 20 are diagonals.
Thus in there are edges.
But n of the edges are not diagonals.