SOLUTION: Let α, β, and γ be the exterior angles of angles A, B, and C of triangle ABC. Show that α + β + γ = 360°.

Question 1132522: Let α, β, and γ be the exterior angles of angles A, B, and C of triangle ABC. Show that α + β + γ = 360°.

Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
.

 = 180° - A

 = 180° - B

 = 180° - C

----------------------------  Add all three equations. You will get

 +  +  = 3*180° - (A + B + C).


Now use  A + B + c = 180°   (the sum of interior angles of a triangle).


Then you will get


 +  +  = 3*180° - 180° = 2*180° = 360°.

QED.

---------------

By the way, for any (convex) polygon, the sum of its exterior angles is equal to 360°.

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