## 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 of a 19 sided polygon?

Regular Polygons

Sides Name Interior Angles
18 Octdecagon 160.00°
20 Icosagon 162.00°
30 Triacontagon 168.00°

## 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 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.

heptacontagon

## How many sides does a polygon have if the sum of its interior angles is 720?

The General Rule

Shape Sides Sum of Interior Angles
Triangle 3 180 °
Pentagon 5 540°
Hexagon 6 720°
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3240 degrees

900°

## What is the sum of the interior angles of a 12 sided polygon?

Using the same methods as for hexagons to the right (I’ll let you do the pictures) So, the sum of the interior angles of a dodecagon is 1800 degrees .

180°

## What does sum of interior angles mean?

Sum of Interior Angles Formula This formula allows you to mathematically divide any polygon into its minimum number of triangles. Since every triangle has interior angles measuring 180° , multiplying the number of dividing triangles times 180° gives you the sum of the interior angles .

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 .

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How do you find the measure of each interior angle of an irregular polygon? It’s just that the angles aren’t all congruent, so you can’t divide by n to get the individual measures . 2) You can use the (n – 2)*180 formula to find both the sum of the interior angles of an irregular […]