how many diagonals does a 62 - sided convex polygon have ?
"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 ca n ' t connect the vertex to itself and we ca n ' 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 a ."
divide(factorial(62), multiply(factorial(subtract(62, const_2)), factorial(const_2)))