How many sides does a regular polygon have if each of its interior angles is $ 165^{\circ} $?


We know that,

For a regular n-sided polygon:

Each interior angle = 180−(360°n\frac{360\degree }{n})

Given that,

Each interior angle measures 165°.

Let the number of sides be n.

Therefore,

165°=180°(360°n)360°n=180°165°360°n=15°n=360°15°n=24 \begin{array}{l}
165\degree =180\degree -\left(\frac{360\degree }{n}\right)\\
\\
\frac{360\degree }{n} =180\degree -165\degree \\
\\
\frac{360\degree }{n} =15\degree \\
\\
n=\frac{360\degree }{15\degree }\\
\\
n=24
\end{array}



Updated on: 10-Oct-2022

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