Question 580179: I know that the equation to find the sum of the measures of the angles for a regular polygon is
(180)N-360 when N=Number of sides. But I do not understand why.
Why do you multiply N by 180 then subtract 360.
Thanks.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! I know that the equation to find the sum of the measures of the angles for a regular polygon is
(180)N-360 when N=Number of sides. But I do not understand why.
Why do you multiply N by 180 then subtract 360.
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It's the same as 180*(n-2) = sum of angles
= 180*n - 360
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If n = 3, 540 - 360 = 180 for a triangle.
If n = 4, 720 - 360 = 360 for a rectangle.
Don't argue with what works.
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The why is harder to explain.
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I can do it on paper and scan it.
The other tutor didn't explain why there are 180 degs in a triangle.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
The other tutor said "Don't argue with what works". I agree but
that's not what you did. You aksed WHY it works, and you are to be
commended for asking that question, not criticized!!!
Here is the answer to your question:
Any polygon can be divided up into triangles. The number of triangles
is always two less triangles than the number of sides of the polygon.
For instance, take this 5-sided polygon (called a "pentagon", like the buiding
in Washington DC):
If you pick any vertex and draw the diagonals,
like this:
the polygon is divided into three triangles (two less
than five). The interior angles of the 3 triangles are
180° each. So the sum of the interior angles of the
polygon is 3 times 180°. That's
the number of sides, 5, minus 2, or 3 times 180°, and if the
number of sides is n, then that's
(n - 2)180°
But as the other tutor explained, if you use the
distributive principle, you get:
n·180° - 2·180°
and that becomes
180°n - 360°
Edwin
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