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In this video we are going to look at exterior angles of polygons. Exterior angles are a little strange. They make a straight line with the interior angle, rather than being the whole outside angle. There are a few different ways to calculate exterior angles. Firstly we can make use of our interior angle knowledge and combine it with the fact that interior and exterior angles make a straight line. To find exterior angles using this method, start by finding the sum of interior angles.

So let's do it for a regular nonagon (9 sided shape). The sum of interior angles of a nonagon = 9 X 7 triangles = 9 X 180 = 1260 degrees. So one interior angle is 1260 divided by 9 sides, which is 140 degrees. The exterior angle will be 180 minus the interior angle, so 180 - 140 = 40 degrees. The second method involves the understanding that if we take all of the exterior angles, and pull them together, they will always make 360 degrees.

This is true for any polygon: the exterior angles will always add up to 360 degrees. We can then use this piece of information to work out how many sides a regular polygon has. If we’re given the exterior angle of 45 degrees, because the exterior angles always add up to 360, we know that 360 divided by the number of sides will equal the exterior angle. And so simple rearranging, 360 divided by exterior angle will give the number of sides. So 360 divided by 45 means this is an octagon. You can either remember it as number of sides = 360 / exterior angle OR exterior angle = 360 / number of sides. So the main points you need to remember are: (1) For the sum of the interior angles, you subtract 2 from the number of sides and multiply it by 180. You can always fit 2 less triangles in. (2) Exterior angles always make 180 degrees with interior angles. And exterior angles always add up to 360 degrees. (3) Combining knowledge of all of these facts, we can work out any interior or exterior angles.

Just make sure if it’s a regular or irregular polygon first!

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