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
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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