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All the interior angles of the polygon form A.P. The common difference is 6 degree..the greatest angle is 135 degree..find the number of sides of polygon.

I try to solve by using n/2[2a+(n-1)d]=(n-2)x180 but I can't solve it. I don't know what is the usage for giving me the greatest angle

Shimin
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  • How do you utilize $135,6$? – lab bhattacharjee Oct 05 '14 at 09:09
  • Oh I realized my mistake..I keep thinking that the common difference is 6 but forgot that the 135 is the greatest angle so others angle should be smaller than 135. hence the commo difference should be -6 – Shimin Oct 05 '14 at 14:49

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We can thinking these angles to be an AP with the first term as $135,$ common difference $=-6$

So, the sum will be $\displaystyle\frac n2[2\cdot135+(n-1)(-6)]^\circ=n(138-3n)^\circ$

Now the sum of angles of $n$ sided polygon is $180(n-2)^\circ$

lab bhattacharjee
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