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Paragraph: The interior angles of a polygon of n sides are in AP. The smallest angle is 120^ and the common difference is 5^ . Question: How many possible values can n have?

Options

  1. AOne
  2. BTwo
  3. CThree
  4. DInfinitely many

Correct answer

A. One

Step-by-step solution

Here, a=120^ and d=5 . Sum of angles of polygon =(n-2) 180^ aligned & n 2 [2 a+(n-1) d]=(n-2) 180 & n 2 [2 120+(n-1) 5]=(n-2) 180 & n^2-25 n+144=0 & (n-9)(n-16)=0 & n=9,16 aligned For n=9, T₉=120+(9-1) 5=160 For n=16, T₁₆=120+(16-1) 5=195 [not possible]

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