Sequences and Series 2 Question 19

20. The interior angles of a polygon are in arithmetic progression. The smallest angle is 120 and the common difference is 5. Find the number of sides of the polygon.

(1980, 3M)

Integer Answer Type Questions

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Solution:

  1. Since, angles of polygon are in an AP.

Sum of all angles

=(n2)×180=n22(120)+(n1)5

5n2125n+720=0n225n+144=0(n9)(n16)=0n=9,16

If n=9, then largest angle =a+8d=160

Again, if n=16, the n largest angle

=a+15d=120+75=195

which is not possible.

[since, any angle of polygon cannot be >180 ]

Hence, n=9

[neglecting n=16 ]



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