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

Answer

We know that the sum of Interior angles of any polygon is $180^{\circ}$.
exterior angles= $180^{\circ}$- $165^{\circ}$$=15^{\circ}$
Given, each exterior angle $=15^{\circ}$
$\therefore \quad$ Number of exterior angles $=\frac{360^{\circ}}{\text { Each exterior angle }}$
$=\frac{360^{\circ}}{15^{\circ}}=24$
Hence, the number of sides of a regular polygon is 24.

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