How many sides does a regular polygon have, if each of its interior angles is 165?

Given :

Each interior angle of a regular polygon is 165°.

To do :

We have to find the number of sides of the polygon.

Solution :

Let the number of sides be 'n'.

The interior angle of a regular polygon with n sides $= 180 - \frac{360}{n}$

Here, the interior angle is 165.

So, $165 = 180 - \frac{360}{n}$

$165 - 180 = - \frac{360}{n}$

$-15 =  - \frac{360}{n}$

$15 \times n = 360$                             [$-$ and $-$ gets cancelled]

$n = \frac{360}{15}$

$n = 24$

Therefore, the number of sides of the regular polygon is 24.

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Updated on: 10-Oct-2022

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