ICSE BoardEnglish MediumSTD 8MATHSUnderstanding Shapes4 Marks
Question
Is it possible to have a regular polygon whose interior angle is : $138^\circ$
✓
Answer
Let no. of sides $=n$
each interior angle $=138^{\circ}$
$\therefore \frac{n-2}{n} \times 180^{\circ}=138^{\circ}$
$ 180 n-360^{\circ}=138 n$
$ 180 n-138 n=360^{\circ}$
$ 42 n=360^{\circ}$
$ n=\frac{360^{\circ}}{42}$
$ n=\frac{60^{\circ}}{7}$
which is not a whole number.
Hence it is not possible to have a regular polygon whose interior angle is $138^{\circ}$.
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