Question

How many non-overlapping triangles can we make in an $n-$gon (polygon having $n$ sides), by joining the vertices?
a) $n-1$
b) $n-2$
c) $n-3$
d) $n-4$

Answer 1

The number of non-overlapping triangles in an $n-$gon $=n-2,$
i.e. $2$ less than the number of sides.

$\begin{array}{cc}\text{No. of sides}& \text{No. of non overlapping triangles}\\ 3& 1\\ 4& 2\\ 5& 3\\ 6& 3\\ .& .\\ .& .\\ .& .\\ n& n-2\end{array}$