Question

2. Answer the following
Find the number of sides of a regular polygon
each of its interior angle is3pie /4radian​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

$\sf \: Interior \: angle \: of \: a \: polygon \: = \: \dfrac{3\pi}{4}$

We know,

$\sf \: Interior \: angle \: + \: Exterior \: angle = \: \pi$

$\sf \: \dfrac{3\pi}{4} \: + \: Exterior \: angle = \: \pi$

$\sf \: Exterior \: angle = \: \pi - \dfrac{3\pi}{4}$

$\sf \: Exterior \: angle = \: \dfrac{4\pi - 3\pi}{4}$

$\bf\implies \:Exterior \: angle \: = \: \dfrac{\pi}{4}$

Now, we know

$\sf \: Number \: of \: sides \:of \: polygon \: = \: \dfrac{2\pi}{ \: Exterior \: angle \:}$

So,

$\sf \: Number \: of \: sides \:of \: polygon \: = \: \dfrac{2\pi}{ \: \dfrac{\pi}{4} \:}$

$\sf \: Number \: of \: sides \:of \: polygon \: = 2\pi \times \frac{4}{\pi}$

$\bf\implies \: Number \: of \: sides \:of \: polygon \: = 8$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\boxed{\begin{array}{c|c} \bf Number \: of \: sides & \bf Sum \: of \: all \: interior \: angles\\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 180 \degree \\ \\ \sf 4 & \sf 360\degree \\ \\ \sf 5 & \sf 540\degree\\ \\ \sf 6 & \sf 720\degree \end{array}} \\ \end{gathered}$

Answer 2

Answer:

number of sides of the given polynomial is 8 i.e. octagon