#### If the sum of the interior angles of a polygon is 540 then how many sides does the polygon have

## How many sides does a polygon have if the sum of its interior angles is 540?

This can be expressed in an equation as: a= 180 (s-2) where a equals the sum of interior angles and s equals the number of sides the polygon has. Therefore we find that the polygon has 5 sides .

## How many sides does a polygon have if the sum of the interior angles is 1080?

8 sides

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

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n – 2) * 180. To find the measure of one interior angle , we take that formula and divide by the number of sides n: (n – 2) * 180 / n.

## How do you find the interior angle of a polygon with 5 sides?

Here’s a pentagon, a 5 – sided polygon . From vertex A we can draw two diagonals which separates the pentagon into three triangles. We multiply 3 times 180 degrees to find the sum of all the interior angles of a pentagon, which is 540 degrees.

## How many sides does a polygon have if the sum of the interior angles is 3600?

How many sides does the polygon have? Solution: (n-2)180=3600, so n-2=20, so s= 22 . Recall that a regular polygon is a polygon in which all of the sides have the same length and all of the angles have the same measure. Example: What is the measure of an interior angle of a regular hexagon?

## What is the sum of the measures of the interior angles of a 13 sided polygon?

Question 130236: What is the sum of the measures of the interior anles of a convex 13 -gon? There is a formula the sum of the measures of the interior angles of a convex n-gon is (n-2)180 degrees. For a triangle, n=3, so it’s (1)180=180 degrees.

## What is the sum of the measure of the interior angles of a 12 Gon?

So, the sum of the interior angles of a dodecagon is 1800 degrees . All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the angles, we know that the sum of all the angles is 1800 degrees (from above) And there are twelve angles

## What is the sum of the measures of the interior angles of a 14 sided polygon?

Here n = 14 , so the sum of the interior angles of a polygon with 14 sides = 2160 deg. Sum of measures of interior angles of a regular polygon =(2n-4)right angles .

## 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 15 sided polygon?

Each triangle has an angle sum of 180 degrees , so the sum of the interior angles of the 15-gon must be 13 × 180 = 2340 degrees . Since the 15-gon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of 2340 ÷ 15 = 156 degrees . an octagon we can draw 5 diagonals.

## What is the sum of the interior angles of an n sided polygon?

Interior and exterior angle formulas: 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 a 6 sided polygon?

The General Rule

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

Triangle | 3 | 180° |

Quadrilateral | 4 | 360° |

Pentagon | 5 | 540° |

Hexagon | 6 | 720° |

## What is a polygon with 5 vertices and 3 sides?

Sides | Name |
---|---|

3 | Triangle |

4 | Quadrilateral |

5 | Pentagon |

6 | Hexagon |

## What is the measure of an exterior angle of a 13 sided polygon?

Regular Polygons

Sides | Name | Exterior Angles |
---|---|---|

10 | Decagon | 36.00° |

11 | Hendecagon | 32.73° |

12 | Dodecagon | 30.00° |

13 | Triskaidecagon | 27.69° |