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

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Question 1079028: Prove that the sum of all three reflex exterior angle is always 900°.
Answer by Edwin McCravy(20060) About Me  (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