#### What is the sum of the interior angles of the polygon shown below?

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

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°.

## What is the sum of the interior angles in a 10 sided polygon?

In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, “ten angles “) is a ten- sided polygon or 10 -gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.

## What is the sum of the interior angles of an n Gon?

The sum of the measures of the interior angles of an n – gon is sum = ( n 2)180˚.

## What is the formula for interior angles?

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 angle sum of a 7 sided polygon?

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.

## What is the sum of the interior angles of a 9 sided polygon?

The General Rule

Shape | Sides | Sum of Interior Angles |
---|---|---|

Octagon | 8 | 1080° |

Nonagon | 9 | 1260° |

.. | ||

Any Polygon | n | (n−2) × 180° |

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

900°

## What is the interior angle of a 14 sided polygon?

154.29°

## What is the sum of interior angles?

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 the interior angles of a 12 Gon?

1800°

## What is the sum of interior angles in a decagon?

1440°

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

720°

## Why is the sum of interior angles of a polygon 180 n 2?

A quadrilateral can therefore be separated into two triangles. If you look back at the formula, you’ll see that n – 2 gives the number of triangles in the polygon , and that number is multiplied by 180 , the sum of the measures of all the interior angles in a triangle. It gives us the number of triangles in the polygon .

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

1260°