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The interior angle measures of a pentagon form an arithmetic progression. The difference between the largest and smallest angle measures is 44 degrees. Find the measure of the smallest angle, in degrees.

SparshGarg  May 16, 2018
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If the difference in the largest and smallest angle is 44 degrees.....then  the common difference between each successive angle measure is 11°

 

And the sum of the angle measures  is 540°

 

Let n   be the smallest angle....so we have

 

n +  (n + 11) + (n + 22)  + (n + 33)  + (n + 44)   = 540     simplify

 

5n  + 110  =   540       subtract  110  from both sides

 

5n  = 430      divide both sides by 5

 

n  = 86° =   the smallest angle

 

 

cool cool cool

CPhill  May 16, 2018

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