# What is the sum of the interior angles of a polygon?

## What is the sum of the interior angles of a polygon?

To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.

### What is the sum of interior angles of a polygon of N sides?

180
The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

Do all polygons add up to 360?

The sum of exterior angles in a polygon is always equal to 360 degrees. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon.

What is the sum of the interior angles of pentagon?

540°Pentagon / Sum of interior angles

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

Answer: The sum of the interior angles of a pentagon is 540° (5 – 2) × 180 = 540°.

### How many sides have a polygon if the sum of its interior angles equals the sum of its exterior angles?

How many sides does the polygon have? The sum of the exterior angles of any polygon is 360 deg irrespective of the number of sides. In the present case the sum of the interior angles is twice the sum of the exterior angles or 720 deg, Thus the polygon in the present case has 6 sides and 6 angles whose sum is 720 deg.

What is the sum of all interior angles of a polygon of 7 sides?

900°
Properties of Heptagon It has seven sides, seven vertices and seven interior angles. It has 14 diagonals. The sum of all interior angles is 900°. The sum of the exterior angles is 360°.

What is the sum of interior angles of a pentagon?

## Do all polygons add up to 180?

A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees. As a result, the interior angles of a regular polygon are all equal to 180 degrees minus the measure of the exterior angle(s).

### What is the sum of the interior angles of a polygon having 8 sides?

1080 degrees
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent.

What is interior angle of pentagon?

108°Pentagon / Internal angle

What is the sum of interior angles of a polygon?

And we also know that the sum of all of those interior angles are equal to the sum of the interior angles of the polygon as a whole. And to see that, clearly, this interior angle is one of the angles of the polygon.

## How do you find the angle of a hexagon?

Hexagon has 6, so we take 540+180=720. A heptagon has 7 sides, so we take the hexagon’s sum of interior angles and add 180 to it getting us, 720+180=900 degrees. Same thing for an octagon, we take the 900 from before and add another 180, (or another triangle), getting us 1,080 degrees.

### What are the measures of the interior angles of a triangle?

So the way you can think about it with a four sided quadrilateral, is well we already know about this– the measures of the interior angles of a triangle add up to 180. So maybe we can divide this into two triangles.