Acertain polygon has a total of five diagonals that can be drawn from all vertices. how many sides would that polygon have? select one: a. 2 b. 7 c. 5 d. 3

5 vertices

Step-by-step explanation:

We know that the total number of diagonals of n vertices of a polygon is given by

Number of diagonal = 5

Hence, d = 5

Plugging this value in above mentioned formula, we get

n can't be negative because it represents the vertices.

Hence, n = 5

c is the correct option.

C. 5

Step-by-step explanation:

We are given that the polygon has total 5 diagonals.

It is known that the formula for the number of diagonals in a polygon is,

Number of diagonals = , where n is the number of sides.

As, the total number of diagonals in the given polygon are 5.

So, we get,

5 =

i.e.

i.e.

Since, the solution of a quadratic equation is given by,

We have,

implies a= 1, b= -3 and c= -10.

So, the solution is,

i.e.

i.e.

i.e.

i.e.  and i.e.

i.e.  and i.e.

i.e. n= 5 and n= -2.

As, the number of sides cannot  be negative.

So, n= 5.

Thus, the polygon will have 5 sides.