r ur question is :
a polygon has 135 diagonals determine the number of side polygon*? bcs if so:
18 sides
Step-by-step explanation:
by using formula
d=n(n-3)/2 where d is no. of diagonals and n is no. of sides of a polygon.
Diagonal =135
Solution :–
135=n(n-3)/2
135(2)=2(n-3)
270=n(square) -3n
n (square)-3n-270=0
(n+15)(n-18)=0
n= -15;n=18 ==> Thus, we don't have any negative side.So, the number of sides are 18.
Check:–
n=18
d=n(n-3)/2
135=( (18) (18-3) ) /2
135=( (18) (15) ) /2
135=270/2
135=135
L. H. S. = R. H. S.
A regular polygon that has 18 number of sides is known as Octakaidecagon.
