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he exterior angles of a k-sided polygon form an arithmetic sequence. The smallest and largest interior angles of the polygon are 136 degrees and 145 degrees. What is k?

 Jun 11, 2022
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Because we are given that the exterior angles form an arithmetic series, the interior angles must as well. 

 

Let d be the common difference in the series, and let k denote the number of turns.

 

We have the equation: \(136 + (k-1)d = 145\)

 

This means \((k - 1)d = 9 \), where both k and d must be integers

 

Can you take it from here?

 Jun 12, 2022

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