Geometry

 

   What is the measure (in degrees) of the smallest [b]interior[/b] angle of a triangle     

   in which the exterior angle measures have the ratio 4:2:8?     

 

   The exterior angles of any polygon always sum to 360^o.     

   So the exterior angles are (⁴/₁₄)(360), (²/₁₄)(360), and (⁸/₁₄)(360).     

   The largest exterior angle would have the smallest interior angle.     

   Therefore, the smallest interior angle is 180 – (⁸/₁₄)(360) degrees.     

   Doing the arithmetic gives us that the smallest angle is – 25.71^o.     

   A triangle can't have a negative angle, so this triangle cannot exist.     

   _.