If a polygon has 42 sides, how many diagonals does it have?
If you connect any vertex to any other vertex besides the 2
next to it, you will get a diagonal.
Every vertex is a connected pair of vertices. However, not
every connected pair of vertices are diagonals.
But first we calculate the number of all pairs of vertices.
That's 42C2.
However, this is too many because each side is also
a connected pair of vertices.
(Note: If you connect a vertex to either of the two
vertices on each side of it, you will NOT get
a diagonal, but you will only retrace two sides of
the polygon.)
So we must subtract the 42 sides from the total number
of vertex pairs, for the 42C2 counts them, too.
Answer: 
Edwin
