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Prove that the sum of the orange angles is 360 degrees.

 

 Feb 21, 2021
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The  sum of the  interior angles of the  quadrilateral  in the  center = 360°

Call these angles  A, B , C  and  D

 

And  each of these angles is supplemental to an exterior angle of a triangle

Call  these angles  (180 - A) , (180 - B) , (180 - C)  and (180  - D)

 

And by the exterior angle theorem, each  of these exterior  angles is equal to the  sum of the two remote  interior  orange angles  in  their respective triangles 

 

So....the  sum   of  all  the orange  angles =  (180 - A) + (180 - B)  + (180 - C) + (180 - D)  =

 

4(180)   - (A + B + C + D)   =

 

720   - 360   =

 

360°

 

 

cool cool cool

 Feb 21, 2021

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