Question

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be $70$ then the number of diagonals of the polygon is

• A. 20
• B. 28
• C. 8
• D. None of these

Answer 1

Answer: (A)

20

Answer 2

A combination of four vertices is equivalent to one interior points of intersection of diagonals.
$\therefore$ No. of interior points of intersection
$={ }^{n} C_{4}=70$
$\Rightarrow n(n-1)(n-2)(n-3)=5.6 .7 .8$
$\therefore n =8$
So, number of diagonals $={ }^{8} C_{2}-8=20$