Question 1079028
<pre><b>

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

{{{drawing(200,200,-1, 5,-1,5, triangle(0,0,1,3,4,0),
red(arc(0,0,1,-1,69,360),arc(4,0,1,-1,180,495),
arc(1,3,1,-1,315,612)

),locate(0,0,A),locate(4,0,B),locate(1,3.36,C)

 )}}} 





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</pre></b>