Question

a convex polygon has 65 diagonals. find the number of sides of the polygon.

Answer 1

The number of sides of the polygon which has 65 diagonals is 13

Answer 2

To find the number of diagonals in a polygon with n sides, use the following formula:[(n)(n-3)/2]

So [(n)(n-3)/2]=65

(n)(n-3)=130

n^2+3n-130=0

n^2+10n-13n-130=0

n(n+10)-13(n+10)=0

(n-13)(n+10)=0

So n={13,-10}

Since there could be no polygon having -10 side 

Therefore polygon of 13 sides have 65 diagonals.