Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals2 Marks
Question
How many sides does a regular polygon have if each of its interior angles is $165^\circ ?$
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Answer
$\because $ Each interior angle $= 165^\circ $
$\therefore $ Each exterior angle $= 180^\circ – 165^\circ = 15^\circ $
Let the number of sides be $n.$ Then,
$n(15^\circ ) = 360^\circ $
$ \Rightarrow n = \frac{{360^\circ }}{{15^\circ }} = 24^\circ $
Hence, the number of sides is $24.$
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