hexagon

 

Five angles of a hexagon measure 119°, 129°, 140°, 129°, and 95°. What is the measure of the sixth angle?   x 

 

The sum of the interior angles of any polygon with n sides can be calculated as 180^o • (n – 2)  

 

The sum of the interior angles of a hexagon is 180^o • (6 – 2)  =  720^o    That's for all six angles.  

 

The other five angles 119^o + 129^o + 140^o + 129^o + 95^o  total  612^o   

 

So by subtraction,  720^o – 612^o  =  108^o  is the size of the sixth angle.  

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