Question

How many sides does a regular polygon have if each of its interior angle is 165°​

Answer 1

Answer:

Number of sides = 24

Step-by-step explanation:

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{internal \: angle \: of \: regular \: polygon = 165} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{number \: of \: sides}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

We know that

$\boxed{ \purple{\bf \:  exterior \: angle = 180 \degree \: - interior \: angle}}$

$\blue{\tt\implies \: \: exterior \: angle \: = 180 \degree - 165 \degree = 15 \degree}$

Now,

We know that

$\boxed{ \red{\tt \:  number \: of \: sides = \dfrac{360 \degree}{exterior \: angle} }}$

$\green{\tt\implies \:number \: of \: sides = \dfrac{360 \degree}{15 \degree} = \bf \: 24}$