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The exterior angles of a k-sided polygon form an arithmetic sequence. The smallest and largest interior angles of the polygon are 136 degrees and 176 degrees . What is k?

 Apr 19, 2021
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Equating  sums for  the interior angles, we  have  that

 

( 136  +176) (k/2)  =  180 (k - 2)   simplify

 

(312)k/2 =  180k - 360

 

156k  = 180k - 360

 

180k  -156k  = 360

 

24k  = 360

 

k =   360  /24   =   15 

 

cool cool cool

 Apr 19, 2021

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