The number of diagonals in a certain regular polygon is equal to five times the number of sides. How many sides does this polygon have?

Lightning Dec 1, 2018

#2**+1 **

The number of diagonals in a regular polygon of n sides = n(n - 3) / 2

So

n(n - 3) / 2 = 5n multiply boh sides by 2

n(n -3) = 10n simplify

n^2 - 3n = 10n subtract 10n from both sides

n^2 - 13n = 0 factor

n ( n - 13) = 0

Set each factor to 0 and solve for n and we get

n= 0 [ reject] or n = 13

So....13 sides

CPhill Dec 1, 2018