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

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## Question

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.

Steps:

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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