Angles of a TriangleDate: 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 |
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