# Polygon Angles

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- Created by: Bhavik
- Created on: 05-06-11 16:10

First 265 words of the document:

Easy Ways to Calculate Polygon angles

Back to angles again, and you thought that you'd heard the last of them!

Interior Angles

You know now that all the interior angles of a triangle add up to 180o. You can

use this gem of knowledge to make working out interior angles in other polygons

really easy.

The quadrilateral below has been split into 2 triangles with the red line. The

curved bits in case you were wondering are supposed to represent the angles.

If we have 2 triangles making up this shape, the sum (total) of the interior angles

= 2 x 180 = 360o.

The same trick applies to other polygons, for example:

Here the sum of the interior angles = 3 x 180 = 540o.

There is a pattern emerging here...look at the number of sides on the first picture

and compare it to the number of triangles.

First Picture: No. of sides = 4, No. of triangles = 2

Second Picture: No. of sides = 5, No. of triangles = 3

A polygon with 6 sides has 4 triangles, one with 7 sides has 5 triangles.

We can create a formula from this which will quickly tell us the number of

triangles which will be found in a polygon of any number of sides. Writing down

the formula in words we say:

The Sum of a Polygon's interior angles = The number of sides minus 2 multiplied

by 180.

Using the shorthand letter n to represent the number of sides we get the formula:

Sum of interior angles = (n 2) x 180.

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