Question

Is it possible to have a regular polygon whose each interior angle is :

(i) ${170}^o$

(ii) ${138}^o$

Answer 1

(i) No. of sides = n

each interior angle $={170}^o$

$\therefore \frac{(n-2)}{n}\times {180}^o={170}^{o}180n-{360}^o=170n180n-170n={360}^{o}10n={360}^{o}n=\frac{{360}^o}{10}n=36$

which is a whole number.

Hence it is possible to have a regular polygon

Whose interior angle is ${170}^o$

(ii) Let no. of sides $={138}^o$

$\therefore \frac{(n-2)}{n}\times {180}^o={138}^{o}180n-{360}^o=138n180n-138n={360}^{o}42n={360}^{o}n=\frac{{360}^o}{42}n=\frac{{60}^o}{7}$

which is not a whole number.

Hence it is not possible to have a regular polygon having interior angle of ${138}^o$.