You can use the formula/theory that the sum of the degrees of the vertices is equal to twice the number of edges. This is because the degree is the number of edges touching the vertex, so adding the degrees of the vertices gives you each time an edge touches a vertex. Since every edge touches two vertices, this counts every edge exactly twice (once at each of the two vertices it connects). Applying that to this question, each vertex has degree four and there are 45 vertices, so 4*45 = 2* (number of edges). Thus there are ninety edges.

May 11th, 2015

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