How many diagonals can be drawn by joining the angular points of an octagon?
8c2 - 8 = 20
Draw an octagon, select one vertex and construct each diagonal from this vertex.You will see there are 5 such diagonals.
Thus for each of the 8 vertices you can draw 5 diagonals and hence you have constructed $5 * 8 = 40$ diagonals. But you have constructed each diagonal twice, once from each of its ends. Thus there are $20$ diagonals in a octagon.
The formula to find the number of sides of a polygon is n(n-3)/2 where “n” equals the number of sides of the polygon. Using the distributive property this can be rewritten as (n2 - 3n)/2. You may see it either way, both equations are identical.