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The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures 128 degres, what is the measure of the smallest angle?

 Aug 3, 2022
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The sum of the interior angles = 360

 

So

 

(128 - 3d) + (128 - 2d ) + (128 - d) + 128  =   360

 

4 (128) - 6d  = 360

 

4 (128) - 360  =  6d

 

152  =  6d

 

d = 152 / 6  =  76/3 

 

The smallest angle =    (128 - 3(76/3) )  =  128 - 76  =   52°   (as we might have guessed....it should be supplemental to 128°)

 

 

cool cool cool

 Aug 3, 2022

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