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Angles of a Triangle

Date: 02/04/2003 at 12:04:48
From: Stephanie
Subject: The angles of a triangle

Dear Dr. Math,

Why do the angles of a triangle always add up to 180 degrees?


Date: 02/04/2003 at 14:40:14
From: Doctor Edwin
Subject: Re: The angles of a triangle

Hi, Stephanie.

Here's one way to explain it that might help. I take a triangle and 
cut one of the sides in half, then open it up so each of the angles is 
180 degrees:


   -------*-----------*----------*-----
          A           B          C

Now the angles on the top (which used to be the inside) and the 
bottom (which used to be the outside) are the same, 180 each, right?

So the sum of the angles on the "inside" is now 540 degrees, just 
as it is on the "outside."

Now watch what happens when we fold it back into a triangle. We've 
twisted it around a complete circle. To do that we've increased the 
total of the OUTSIDE angles by 360 degrees - one circle's worth. So 
the total of the INSIDE angles must have decreased by the same amount. 

If the total is 540 to start with and we subtract 360, how big is it 
now?

Does this help? Write back if you need to.

- Doctor Edwin, The Math Forum
  http://mathforum.org/dr.math/ 


Date: 02/05/2003 at 11:20:30
From: Stephanie
Subject: Thank you (The angles of a triangle)

Thank you for answering my question. I now understand why  the angles 
of a triangle are always 180 degrees.

Stephanie
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

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