How many diagonals does a 61-sided convex polygon have?  Options.
A) 1182
B) 1769
C) 2456
D) 3538
E) 4209
A 61-sided convex polygon has 61 vertices.   If we examine a single vertex, we can see that we can connect it with 58 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 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be (61)(58) = 3538   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3538 by 2 to get 1769.   The answer is 1769.
<result>B</result>
How many diagonals does a 61-sided convex polygon have?