The Pentagon is an attractive five sided shape that you have probably seen many times used in conjunction with its six sided colleague when you look at a standard football.  Usually the hexagons are white and the pentagons are black.


Let’s take a look at the Pentagon now:





By simple addition you can see that the internal angles do in fact add up to 540° as I mentioned before, but if you see the external angle shown in this particular shape for the first time which is 72° you will realise that five of these does in fact add up to 360°.  As we move to hexagon, heptagon, octagon and so on you will see that the internal angles will add up to ever-increasing numbers but the external angles will still add up to 360°.