Is it possible to have a polygon, whose sum of interior angles is $1030^\circ .$
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Answer
Let no. of. sides be $= n$
Sum of interior angles of polygon $= 1030^\circ$
$\therefore (2n - 4) \times 90^\circ = 1030^\circ$
$\Rightarrow 2( n -2)=\frac{1030^{\circ}}{90^{\circ}}$
$\Rightarrow( n -2)=\frac{1030^{\circ}}{2 \times 90^{\circ}}$
$\Rightarrow( n -2)=\frac{103}{18}$
$\Rightarrow n =\frac{103}{18}+2$
$\Rightarrow n =\frac{139}{18}$
Which is not a whole number.
Hence it is not possible to have a polygon,
the sum of whose interior angles is $1030^\circ .$
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