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A nonagon has angles that measure 140°, 140°, 130°, 140°, 140°, 145°, 155°, 140°, and a. What is a?    

 

You would calculate the sum of all the angles,   

then subtract the total of the angles you know.   

 

The sum of the internal angles of a polygon is  S = (n – 2)(180^o)    

where n is the number of sides of the polygon.  

 

                                                             S  =  (9 – 2)(180^o)   

                                                             S  =  7 • 180^o   

                                                             S  =  1260^o   

 

The total of the known angles is                    1130^o   

if neither of us made a mistake.  

You'd better check my addition.   

 

Subtract                                                 a  =  130^o     

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