Exterior Angles in TrianglesDate: 09/11/99 at 20:08:47 From: Kimberly Subject: Exterior angles Dear Dr. Math, I'm a sophomore taking 11th grade math and right now I'm trying to figure out how to prove that in any triangle, each exterior angle is equal to the sum of the two nonadjacent interior angles. Here's what the problem looks like: S / /d I have to prove that d = b + c Q /a\ / \ / \ / \ / \ / \ /b c\ P---------------R Thanks for your help, Kimberly Date: 09/18/1999 at 15:04:50 From: Doctor Lilla Subject: Re: Exterior angles Dear Kimberly, Thanks for writing to Dr. Math. You have included a very nice drawing here to explain your question, so I can see that you understood the problem. You understood the terms "exterior" and "interor" angles, too. Fortunately this problem is not as hard as it seems to be. I assume you know that the sum of the 3 interior angles in every triangle is 180 degrees. So: a + b + c = 180 Next, we should realize that a and d are supplementary angles, so their sum is 180. a + d = 180 Try to compare these equations, and after some algebraic steps you should get a proof of your problem. I hope it helps you, and that you can finish from here. Please write back if you still have questions. - Doctor Lilla, The Math Forum http://mathforum.org/dr.math/ |
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