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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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