Question

There are 44 diagonals in a polygon then number of sides in polygon is:

(a) 11

(b) 7

(c) 8

(d) None of these

Answer 1

Correct answer is 11.

Suppose you have n points in a plane making a polygon. In order to create a diagonal you will have to select any one point (from n points), and then select another point which is not adjacent to the previously selected point (n-3 choices).

ⁿC₁ × ^n-3C₁

In this expression we are gonna have repeated diagonals (Eg: AB is no different from BA), so we'll divide it by 2

ⁿC₁ × ^n-3C₁ = 2 × 44

n × (n-3) = 11 × 8

n = 11

No. of points = No. of sides = 11

Answer 2

Correct option is (a) 11