# How many diagonals are there in a pentagon with formula?

## How many diagonals are there in a pentagon with formula?

pentagon has 5 diagonals on the inside of the shape. The diagonals of any poygon can be calculated using the formula n×2(n−3) where n is the number of sides, in case of a pentagon which “n” will be 5, the formula as expected is equal to 5.

## What is the formula of a diagonal?

The formula to calculate the number of diagonal of an n-sided polygon = n(n-3)/2 where n is the number of sides of the polygon.

**What is the formula to find the diagonal of a polygon?**

The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).

**How do you find the number of sides?**

Subtract the interior angle from 180. For example, if the interior angle was 165, subtracting it from 180 would yield 15. Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon.

### How do you find the diagonal of a shape?

The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides. To find the total number of diagonals in a polygon, multiply the number of diagonals per vertex (n – 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice).

### How do you calculate diagonal?

You can use the Pythagorean theorem to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w² , and now you should know how to find the diagonal of a rectangle explicit formula – just take a square root: d = √(l² + w²) .

**What is polygon formula?**

Formula 1: The sum of interior angles of a polygon with “n” sides = 180°(n-2) Formula 3: The measure of each interior angle of a regular n-sided polygon = [(n-2)180°]/n. Formula 4: The measure of exterior angles of a regular n-sided polygon = 360°/n.

**How do you find the number of sides of a regular polygon?**