Sum of Angles of Polygon...

Date: 9/24/96 at 16:34:13
From: Scott Thompson
Subject: Sum of Angles of Polygon...

I need help with a proof.

1) Assuming the equality of alternate interior angles formed by a 
   transversal cutting a pair of parallel lines, prove:

   a) The sum of the angles of a triangle is equal to a straight 
      angle.

   b) The sum of the interior angles of a convex polygon of n sides 
      is equal to n-2 straight angles.

This is my drawing:   

                         /  
------------------------/--------                                                 
                       /                        
----------------------/----------
                     /

Thanks for any assistance,
Scott

Date: 10/21/96 at 15:36:0
From: Doctor Jaime
Subject: Re: Sum of Angles of Polygon...

Here's another drawing:

    

>a) The sum of the angles of a triangle is equal to a straight angle.

Draw any triangle. Draw a parallel to one of the sides. Now you can 
use 1) twice to show that the angles relative to the chosen side equal 
two of the angles drawn under the parallel line. Now do you see the 
sum of the angles of a triangle is equal to a straight angle?

>b) The sum of the interior angles of a convex polygon of n sides 
>   is equal to n-2 straight angles.

Here's a hint: try to divide the polygon into triangles and use a). 
Can you do it now? Let us know if you need more help.

-Doctor Jaime,  The Math Forum
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