# How To Find Interior Angles Of A Polygon?

## How do you find the interior and exterior angles of a polygon?

Finding Interior and Exterior Angles in a Polygon –

## How do you find the number of sides in a polygon with a given interior angle?

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 interior angle of a polygon when given the exterior angle?

Given one exterior angle, learn how to find the number of sides of a

## What is the formula for finding interior angles of a polygon?

An interior angle is located within the boundary of a polygon. The sum of all of the interior angles can be found using the formula S = (n – 2)*180. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides.

## What is the interior and exterior of an angle?

In summary, we learned that an interior angle is an angle inside a shape, while an exterior angle is an angle made by the side of a shape and a line drawn out from an adjacent side. The sum of the interior angles of a triangle is always 180.

## What is the formula of polygon?

Measure of a Single Interior Angle

Shape Formula Sum interior Angles
Regular Pentagon (3−2)⋅180 180∘
4 sided polygon (quadrilateral) (4−2)⋅180 360∘
6 sided polygon (hexagon) (6−2)⋅180 720∘

## How many sides does a regular polygon have if the interior angle is 160?

If the interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.

6 sides

## Can it be an interior angle of a regular polygon Why?

If 22° is an interior angle, then 180° – 22°, i.e. 158° is exterior angle. Thus, 22° cannot be an interior angle of a regular polygon.

## What is the exterior angle of a polygon?

An exterior angle of a polygon is an angle at a vertex of the polygon, outside the polygon, formed by one side and the extension of an adjacent side. Notice that corresponding interior and exterior angles are supplementary (add to 180°). Exterior angles of a regular polygon are equal in measure.

12 sides

## What is the formula of interior angle of polygon?

An interior angle is located within the boundary of a polygon. The sum of all of the interior angles can be found using the formula S = (n – 2)*180. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides.

## Is a circle a polygon?

Polygons. A polygon is a closed plane figure with three or more sides that are all straight. A circle is not a polygon as it does not have straight sides.

## What is the formula of regular polygon?

You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.