Question

The number of sides of a regular polygon is given. Find the measure of each interior angle of each polygon.

$\left(i\right)$ $7$ $\left(ii\right)$ $9$ $\left(iii\right)$ $11$ $\left(iv\right)$ $15$ $\left(v\right)$ $17$

Answer 1

$\Rightarrow$ Measure of each interior angle of regular polygon $=\frac{2n-4}{n}\times {90}^o.$

$\left(i\right)$ Measure of each interior angle of regular polygon having $7$ sides $=\frac{(2\times 7)-4}{7}\times {90}^o.$

$=\frac{10}{7}\times {90}^o$

$={128.57}^o$

$\left(ii\right)$ Measure of each interior angle of regular polygon having $9$ sides $=\frac{(2\times 9)-4}{9}\times {90}^o.$

$=\frac{14}{9}\times {90}^o$

$={140}^o$

$\left(iii\right)$ Measure of each interior angle of regular polygon having $11$ sides $=\frac{(2\times 11)-4}{11}\times {90}^o.$

$=\frac{18}{11}\times {90}^o$

$={147.27}^o$

$\left(iv\right)$ Measure of each interior angle of regular polygon having $15$ sides $=\frac{(2\times 15)-4}{15}\times {90}^o.$

$=\frac{26}{15}\times {90}^o$

$={156}^o$

$\left(v\right)$ Measure of each interior angle of regular polygon having $17$ sides $=\frac{(2\times 17)-4}{17}\times {90}^o.$

$=\frac{30}{17}\times {90}^o$

$={158.82}^o$