SOLUTION: Prove that the sum of three exterior angles of a triangle fromed by producing the sides in order is four right angles or 360°

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Question 1181777: Prove that the sum of three exterior angles of a triangle fromed by producing the sides in order is four right angles or 360°
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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Let  alpha, beta  and  gamma are three interior angles of the triangle.


Then the respective exterior angles are  180%5Eo+-+alpha,  180%5Eo+-+beta  and  180%5Eo+-+gamma.


The sum of exterior angles is then


    180%5Eo+-+alpha + 180%5Eo+-+beta + 180%5Eo+-+gamma = 540%5Eo+-++%28alpha%2Bbeta%2Bgamma%29 = 540° - 180° = 360°,


since the sum of interior angles of any triangle is 180°.

At this point, the proof is completed.