# How do you find the sum of the interior angles of a pentagon?

## How do you find the sum of the interior angles of a pentagon?

The sum of all interior angles of a regular polygon is calculated by the formula S=(n-2) × 180°, where ‘n’ is the number of sides of a polygon. For example, to find the sum of interior angles of a pentagon, we will substitute the value of ‘n’ in the formula: S=(n-2) × 180°; in this case, n = 5.

Why is the sum of the interior angles of a pentagon 540?

Why is this? This is because you can make any pentagon with three triangles. Remember, the 3 angles of any triangle always add up to 180 degrees. So if you have three triangles making up your pentagon, then your angles will always add up to 540 degrees (3 * 180 degrees).

What angles make up a pentagon?

In geometry, a pentagon (from the Greek πέντε pente meaning five and γωνία gonia meaning angle) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°….

Pentagon
Internal angle (degrees) 108° (if equiangular, including regular)

### What is the sum of an irregular pentagon?

Sum of Interior Angles of a Polygon with Different Number of Sides:

Irregular Polygons
Polygon No. of Sides Sum of Interior Angles
Triangle 3 1800
Pentagon 5 5400

What is the sum of a hexagons interior angles?

720°
Hexagon/Sum of interior angles

How the sum of pentagon is 540?

To find the sum of the angles in a pentagon, divide the pentagon into different triangles. Since the sum of the angles of the triangles is equal to 180 degrees. 3 x 180 = 540 degrees. Therefore, the sum of angles in a pentagon is 540 degrees.

## What is the polygon whose sum of the interior angles is 1 080?

octagon
The polygon with an interior angle sum of 1080° is an octagon, or a polygon with 8 sides.

What is the total angle of pentagon?

540 degrees
Angles in a Pentagon

Shape Sides Sum of Interior Angles
Triangle 3 sides 180 degrees
Pentagon 5 sides 540 degrees
Hexagon 6 sides 720 degrees

What is the formula for the interior angles of a pentagon?

The pentagon has 5 interior angles of 108o and 5 exterior angles of 72∘. The exterior angles have a sum of 360∘ = (5)72∘. In order to find the value of the interior angle of a regular polygon, the equation is (n−2)180∘ n where n is the number of sides of the regular polygon.

### What is the total measure of the interior angle of a pentagon?

In the case of a regular pentagon, the interior angle is equal to 108°, and the exterior angle is equal to 72°. An equilateral pentagon has five sides that are equal to each other. The sum of the interior angles of a rectangular pentagon is equal to 540 degrees.

Are all the interior angles of a pentagon equal?

A regular pentagon is a pentagon whose sides are equal in length, and whose interior angles are equal in measure. Since each of the interior angles in a regular pentagon are equal in measure, each interior angle measures 540°/5 = 108° as shown below. Each exterior angle of a regular pentagon has an equal measure of 72°.

How many interior angles does a pentagon have?

A regular pentagon has. 5 equal sides. 5 equal internal angles at the center each equal to 72 deg. 5 equal interior angles where the adjacent sides meet each equal to 108 deg.