Question

Find the number of sides in a regular polygon, if its each interior angle is :

(i) ${160}^o$

(ii) ${135}^o$

(iii) $1\frac{1}{5}$ of a right-angle.

Answer 1

(i) Let no. of sides of regular polygon be n.

Each interior angle $={160}^o$

$\therefore \frac{(n-2)}{n}\times {180}^o={160}^{o}180n-{360}^o=160n180n-160n={360}^{o}20n={360}^{o}n=18$.

(ii) No. of sides = n

Each interior angle $={135}^o\frac{(n-2)}{n}\times {180}^o={135}^{o}180n-{360}^o=135n180n-135n={360}^{o}45n={360}^{o}n=8$.

(iii) No . of sides = n

Each interior angle $=1\frac{1}{5}$ right angles

$=\frac{6}{5}\times 90={108}^o\therefore \frac{(n-2)}{n}\times {180}^o={180}^{o}180n-{360}^o=108n180n-108n={360}^{o}72n={360}^{o}n=5$.