Is the sum of the angles of any polygon 1600deg ?how about 900deg

Dear Student,

Please find below the solution to the asked query:

Given :  Sum of all interior angles of a polygon =  1600$°$

We know " If any polygon have ' n ' sides then sum of interior angle is = ( n - 2 ) $\times$ 180$°$  " .

So,

( n - 2 ) $\times$ 180$°$  =  1600$°$  , Now we divide by 180$°$ both hand side and get

( n  - 2 ) =  8.88  ,

n - 2 = 8.88

n  = 10.88 , But number of sides can't be in fraction so

There is no polynomial that have sum of interior angles is 1600$°$ .                             ( Ans )

And Sum of all interior angles of a polygon =  900$°$

( n - 2 ) $\times$ 180$°$  =  900$°$  , Now we divide by 180$°$ both hand side and get

( n  - 2 ) =  5  ,

n - 2 = 5 ,

n  = 7

Therefore,

Sum of angles is 900$°$ , Then polygon have total number of sides  =  7                                         ( Ans )


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