Question 147275: given an arbitrary triangle,what can you say about the sum of 3 exterior angles, 1 for each vertex of the triangle??
thnx again
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, you can say this!
Let the three angles of the arbitrary triangle be A, B, and C.
First, you know that the sum of these three angles is 180 degrees, so...
A+B+C = 180
Next, the exterior angle of any one of the three interior angles is the supplement of that interior angle, so the sum of the three exterior angles of our arbitrary triangle is:
(180-A)+(180-B)+(180-C) = 540-(A+B+C)
But we said earlier that A+B+C = 180, so, making the substition, we get...
The sum of the three exterior angles is:
540-180 = 360 degrees.
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