How many diagonals does a 60-sided convex polygon have? Choose one.
A) 960 B) 1280 C) 1710 D) 2560 E) 3420
A 60-sided convex polygon has 60 vertices.   If we examine a single vertex, we can see that we can connect it with 57 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 60 vertices can be connected with 57 vertices to create a diagonal then the total number of diagonals would be (60)(57) = 3420   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3420 by 2 to get 1710.   The answer is 1710.
<result>C</result>
How many diagonals does a 60-sided convex polygon have?