



The
angles inside any triangle add up to 180 degrees.












What
about the angles inside a shape with four corners? 











How come
the angles inside a triangle add up to 180 degrees 


and the
angles inside a shape with 4 corners add up to 360 degrees? 





It works
like this ... 





Think of
the line that draws the shape like a sidewalk. 


In any
shape, 


from some
starting point you go one time around a circle 


and end
up back where you started ... 











One
complete turn around equals 360 degrees. 


Yeah, but
the triangle has only 180 degrees. 


Just hold
on, I'm not done yet ... 





To make
the explanation easier, 


we'll use
a triangle with all the same angles 


but it
will work with any triangle. 





So say
you're walking along this sidewalk on the triangle 


and you
come to the first angle (turn). 











Since
there are three angles in the triangle, 


we turn
1/3 of the whole 360 each time we turn. 











So we
turned 120 degrees. 











Now
figure out what's left on the inside ... 











So
there's 60 degrees left on the inside. 


60
degrees times three turns is 180 degrees. 


And there
you are. 





OK, now
let's try a 4 sided shape. 


To keep
things simple, we'll use a square. 


But this
will work with any 4 sided shape ... 











Now try a
pentagon (5 sided). 











OK, let's
stop a second and see what's happening here ... 





Number
of Sides 
Total
of Interior Angles 
3 
180 

4 
360 
(180
+ 180 = 360) 
5 
540 
(360
+ 180) = 540 






Every
time we add another side, 


the
interior angles add up to 180 degrees more. 





That
means we can continue this chart 


as far as
we want really fast. 





Number
of Sides 
Total
of Interior Angles 
3 
180 

4 
360 

5 
540 

6 
720 

7 
900 

8 
1080 







The more
sides (and angles) we have in an object, 


the more
the angles inside the shape add up to! 





We could
even write a formula like this ... 





Angles
inside a polygon add up to = 180 ×
(number of sides  2)






If we
just kept adding more and more sides 


until the
number of sides gets to infinity, 


what
shape would we have? 





A CIRCLE!






copyright 2005 Bruce Kirkpatrick 
