How many diagonals does a 58-sided convex polygon have?
Pick:  A) 870  B) 1125  C) 1595  D) 2560  E) 3190
A 58-sided convex polygon has 58 vertices.   If we examine a single vertex, we can see that we can connect it with 55 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.   If each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be (58)(55) = 3190   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3190 by 2 to get 1595.   The answer is 1595.
<result>C</result>
How many diagonals does a 58-sided convex polygon have?