ICSE BoardEnglish MediumSTD 8MATHSUnderstanding Shapes4 Marks
Question
Is it possible to have a polygon, whose sum of interior angle is: $870^\circ$
✓
Answer
Let no. of sides $=n$
Sum of angles $=870^{\circ}$
$(n-2) \times 180^{\circ}=870^{\circ}$
$n-2=\frac{870}{180}$
$n-2=\frac{29}{6}$
$\mathrm{n}=\frac{29}{6}+2$
$\mathrm{n}=\frac{29}{6}+\frac{2}{1}$
$\mathrm{n}=\frac{29+12}{6}$
$\mathrm{n}=\frac{41}{6}$
Which is not a whole number.
Hence it is not possible to have a polygon, the sum of whose interior angles is $870^{\circ}$.
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