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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 $44^\circ$. Find the measure of the smallest angle, in degrees.

 Oct 21, 2017
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Call the  smallest angle measure, N

 

And the largest  N + 44

 

And the sum of the interior angle measures of a pentagon  = 540°

 

So

N + (N + d) + (N + 2d) + (N + 3d) + (N + 4d)  =  540 

Where d is the common difference....simplifying, we have that

 

5N + 10d  = 540     (1)    and

N + 44  = N + 4d   →  44 = 4d →  11 = d    sub this into (1)

 

5N + 10 (11) = 540

5N + 110  = 540

5N  = 430       divide through by 5

N  = 86°

 

 

cool cool cool

 Oct 21, 2017

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