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## How is the sum of the interior angles of a polygon related to its number of sides?

We know that if a polygon has ‘n’ sides , then it is divided into (n – 2) triangles. We also know that, the sum of the angles of a triangle = 180°. Therefore, the sum of interior angles of a polygon having n sides is (2n – 4) right angles . Thus, each interior angle of the polygon = (2n – 4)/n right angles .

## How many sides does a polygon have with an interior angle of 1620?

So, the sum of the interior angles of an 11-gon is 1620 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 1620 degrees (from above) And there are eleven angles

15 sides

## 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 formula to find the sum of interior angles?

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.

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## How do you figure out how many sides a polygon has?

Finding the Number of Sides of a Polygon You can use the same formula , S = (n − 2) × 180° S = ( n – 2 ) × 180 ° , to find out how many sides n a polygon has , if you know the value of S , the sum of interior angles.

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## How many sides does a regular polygon have if the measure of an exterior angle is 24?

1 Answer. The polygon has 15 sides .

## How do you know if a polygon is convex?

Consider each set of three points along the polygon . If every angle is 180 degrees or less you have a convex polygon . When you figure out each angle, also keep a running total of (180 – angle). For a convex polygon , this will total 360.

## How many sides does a polygon have with an interior angle of 108?

Each interior angle of the polygon is 108 degrees, so each exterior angle of the polygon is 180-108 = 72 degrees. So the number of sides is 360/72 = 5.

## How many sides does a polygon have with an interior angle of 3960?

In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four- sided polygon . The sum of any icositetragon’s interior angles is 3960 degrees.

## What is the sum of the interior angle measures of a polygon with 15 sides?

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.

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