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METHOD 1:
Let's divide some regular polygons
into triangles by connecting one vertex to all of the others...
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A
square has 4 sides and we made 2 triangles.
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A
pentagon has 5 sides and we made 3 triangles.
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A
hexagon has 6 sides and we made 4 triangles.
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Do you see the pattern?
A heptagon has 7 sides... so we'd
be able to make 5 triangles.
If we had polygon with n sides...
we'd be able to make (n - 2) triangles.
Let's start with the square...
We made 2 triangles. Notice that all of the interior angles
of the 2 triangles make up the interior angles of the square.
The sum of the 2 triangle's angles
is 
There are 4 equal
angles in a square,
so 
gives us that one angle of a square is
!
Just what we expected.
Now for the pentagon.
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We made 3
triangles.
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So the interior angles
of a regular pentagon are each 108 degrees.
Can you figure out the hexagon?
How about a 100-gon? (That's a
regular polygon with 100 sides.) There would be 98 triangles...
So, in general, the measure of
an interior angle of a regular n-gon is
Continued on the
next
page
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