Question

Find the number of sides of a regular polygon if each of its interior angles is $\frac{3{\pi }^c}{4}$.

Answer 1

Measure of each interior angle $\frac{3\pi }{4}$

$\Rightarrow \frac{\left(n-2\right)180}{n}=\frac{3\pi }{4}$

$\Rightarrow \frac{(n-2)}{x}\times \pi =\frac{3\pi }{4}$

$\Rightarrow \frac{\left(n-2\right)}{n}=\frac{3}{4}$

$\Rightarrow 4n-8=3n$

$\to n=8$

Sy Number of sides is $8$