The measures of the interior angles in a polygon are consecutive integers. the smallest angle measures 136 degrees. how many sides does this polygon have?

Question

Mathematics

Dylan Russo

29 September, 04:53

The measures of the interior angles in a polygon are consecutive integers. the smallest angle measures 136 degrees. how many sides does this polygon have?

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Answers (1)

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Rebecca Olson · Answer 1

Other than writing an iterative computer program to determine this answer, it can be done manually.

Using N as the number of sides of a polygon, (N-2) 180 = number of degrees of an N-sided polygon. The range from 180 up to 1260 for a 9 sided polygon.

Starting with 136 and adding consecutive numbers to it, the answer turns out to be a 9 sided polygon of 1260 degrees.