Polygon Angles

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  • Created by: Bhavik
  • Created on: 05-06-11 16:10
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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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The brackets are there to make sure that you subtract 2 from n before multiplying
by 180.
Don't try and remember the formula, you don't need to just remember splitting
polygons up into triangles and the formula will appear magically from your
One last thing on interior angles. If you have a regular polygon (pentagon,
hexagon etc.…read more


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