How many diagonals does a 62-sided convex polygon have?  Choose one:  A) 1829  B) 2356  C) 3458  D) 3843  E) 4820
A 62-sided convex polygon has 62 vertices.   If we examine a single vertex, we can see that we can connect it with 59 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 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.   The answer is 1829.
<result>A</result>
How many diagonals does a 62-sided convex polygon have?