SOLUTION: Prove that the sum of all three reflex exterior angle is always 900�.

Question 1079028: Prove that the sum of all three reflex exterior angle is always 900�.
Answer by Edwin McCravy(20062) (Show Source): You can put this solution on YOUR website!



The reflex exterior angles are the outside angles indicated by 
the red arcs in this picture:

 





A reflex angle is 360� minus the acute or obtuse angle with
the same sides.

Let the interior angles of a triangle be A, B, and C.

The sum of the interior angles of any triangle is 180�,
So A+B+C = 180�

Then the reflex exterior angle at vertex A is 360�-A.
Then the reflex exterior angle at vertex B is 360�-B.
Then the reflex exterior angle at vertex C is 360�-C.

The sum of the reflex exterior angles is 

(360�-A)+(360�-B)+(360�-C) = 360�-A+360�-B+360�-C
1080�-A-B-C = 1080�-(A+B+C) = 1080�-180� = 900�

Edwin

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