You can put this solution on YOUR website! the number of diagonals in a polygon are given by the equation:
(n * (n-3))/2
for your decagon, the number of sides is equal to 10.
this makes the formula:
(10 * 7)/2 which becomes 35.
you can see the formula working in smaller polygons.
for a quadrilateral the number of diagonals is clearly 2.
(4 * 1) / 4 / 2 = 2
for a pentagon the number of diagonals is clearly 5
(5 * 2) / 2 = 10 / 2 = 5
for a hexagon the number of diagonals is not so clearly 9 (it's getting harder to count them but the number is definitely 9).
(6 * 3) / 2 = 18 / 2 = 9
see the following reference for more information: http://www.math.com/tables/geometry/polygons.htm
