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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?
Asked by rushabh123 | 20 Nov, 2018, 12:16: PM
If a polygon has n sides, then sum of interior angles is (n-2)×180

Given polygon's smallest interior angle is 136° and they are consecutive integers.
Hence n angles are in A.P with common difference 1

sum of the angles = (n/2)[ 272 +(n-1) ] = (n-2)×180 ..................(1)

By solving eqn.(1), we get n = 9
Answered by Thiyagarajan K | 23 Nov, 2018, 12:39: AM

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