Question

In a polygon there are 12 diagonals through a vertex . How many diagonals are there in all

Answer 1

Answer:90

Step-by-step explanation:

You exclude adjacent sides will drawing diagonals so the polygon is 15 sided.

No.of diagonals=no.of sides[(no.of sides-3)/2]

=15[(15-3) /2]

=15[12/2]

=15*6

=90

Answer 2

Given,

In a polygon, the number of diagonals presents from a single vertex = 12

To find,

The total number of diagonals in the polygon.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

In any polygon;

total number of vertices = total number of sides

{Equation-1}

And, the total number of diagonals in a n-sided polygon = n(n-3)/ 2

{Equation-2}

According to the question;

The polygon has 12 diagonals present from a single vertex

=> The polygon has 12 points to which a single point has its diagonals

=> Total number of vertices in the polygon

= total number of points to which a single point has its diagonals + the common vertex itself + 2 adjacent vertices which firm the corresponding adjacent sides

= 12 + 1 + 2 = 15

=> Total number of vertices in the polygon = 15

=> Total number of sides in the polygon = 15

(according to equation-1)

Now, according to the equation-2;

The total number of diagonals in the given polygon having number of sides, n equal to 15 is

= n(n-3)/ 2

= 15 × (15-3)/2

= 15 × 12/2

= 15 × 6 = 90

Hence, the polygon has a total of 90 diagonals.