ICSE BoardEnglish MediumSTD 8MATHSUnderstanding Shapes4 Marks
Question
Is it possible to have a regular polygon whose interior angle is : $170^\circ$
✓
Answer
No. of sides $=n$
each interior angle $=170^{\circ}$
$\therefore \frac{\mathrm{n}-2}{\mathrm{n}} \times 180^{\circ}=170^{\circ}$
$180 n-360^{\circ}=170 n$
$180 n-170 n=360^{\circ}$
$10 n=360^{\circ}$
$\mathrm{n}=\frac{360^{\circ}}{10}$
$n=36$
which is a whole number.
Hence it is possible to have a regular polygon
whose interior angle is $170^{\circ}$
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