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°.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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°.       Log On


   

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(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
alpha = 180° - A

beta = 180° - B

gamma = 180° - C

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

alpha + beta + gamma = 3*180° - (A + B + C).


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


Then you will get


alpha + beta + gamma = 3*180° - 180° = 2*180° = 360°.

QED.

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