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ICSE Class 10 Answered

The angles of a polygon are in A.P. with common difference 5º. If the smallest angle is 120º, find the number of sides of the polygon.
Asked by shreyashichaudhary012 | 17 Jan, 2019, 09:14: PM
answered-by-expert Expert Answer
smallest angle is 120° means , first term of A.P = 120°
 
if polygon has n sides, then sum of angles using A.P,  (n/2) { 2×120 + (n-1)×5 }  ............(1)
 
but we know, if polygon has n sides, sum of interior angles  = (n-2)×180  ..............(2)
 
By equating(1) and (2) and after simplification we get the expression,   n2 - 25n + 144 = 0 .............(3)
 
By factorising LHS of (3), we have (n-9)(n-16) = 0
 
hence n = 9 or n = 16  . Hence number of sides can be 9 or 16
Answered by Thiyagarajan K | 17 Jan, 2019, 10:21: PM
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