How many diagonals does a 63-sided convex polygon have? Choose one:	A) 1890	B) 1953	C) 3780	D) 3843	E) 3906
A 63-sided convex polygon has 63 vertices.   If we examine a single vertex, we can see that we can connect it with 60 other vertices to create a diagonal. NOTE: there are 60 options because 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 63 vertices can be connected with 60 vertices to create a diagonal then...   ...the total number of diagonals = (63)(60) = 3780   HOWEVER, before we select answer choice C, we must recognize that we have counted every diagonal TWICE.   For example, we might connect vertex A with vertex F and count that as 1 diagonal, and at the same time we connect vertex F with vertex A and count that as 1 diagonal. Of course these diagonals are the SAME.   To account for counting each diagonal twice, we must divide 3780 by 2 to get: 1890   1890NSWER:1890
<result>A</result>
How many diagonals does a 63-sided convex polygon have?