Ex.3.2 Q3 Understanding Quadrilaterals Solution - NCERT Maths Class 8

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How many sides does a regular polygon have if the measure of an exterior angle is \(24^\circ\)?

Text Solution

What is Known?

Measure of an exterior angle is \(24^\circ\).

What is Unknown?

The number of sides of the regular polygon.


Total measure of all the exterior angles of the regular polygon \(= 360^\circ \)

Let number of sides be \(= n\).

Measure of each exterior angle \( = 24^\circ \)

Therefore, the number of sides 

\[\begin{align} &= \,\,\frac{{{\text{Sum of exterior angles}}}}{{{\text{Each exterior angle}}}}\\&= \,\,\,\frac{{360^\circ }}{{24^\circ }}\\&= \,\,\,15\end{align}\]

\(\therefore \) \(R\), regular polygon has \(15\) sides.

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