# Ex.3.2 Q2 Understanding Quadrilaterals Solution - NCERT Maths Class 8

## Question

Find the measure of each exterior angle of a regular polygon of

(i) \(9\) sides

(ii) \(15\) sides

## Text Solution

**What is Known?**

The number of sides of the polygon.

**What is Unknown?**

Exterior angle of a regular polygon of \(9\) sides.

Exterior angle of a regular polygon of \(15\) sides.

**Reasoning:**

Irrespective of the number of sides of the polygon, the measure of the exterior angles is equal and the sum of the measure of all the exterior angles of the regular polygon is equal to \(360^\circ\).

**Steps:**

(i) \(9\) sides

Total measure of all exterior angles \( = {360^{\rm{\circ}}}\)

Each exterior angle

\[\begin{align}&= \frac{{{\text{sum of exterior angle}}}}{{{\text{number of sides}}}}\\&= \,\,\frac{{{{360}^{\rm{\circ}}}}}{9}\\&= \,\,{40^{\rm{\circ}}}\end{align}\]

Each exterior angle \(={\rm{4}}0^\circ \)

(ii) \(15 \) sides

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

Each exterior angle

\[\begin{align}&= \frac{{{\text{sum of exterior angle}}}}{{{\text{number of sides}}}}\\&= \frac{{{{360}^{\rm{\circ}}}}}{{15}}\\&= \,{24^{\rm{\circ}}}\end{align}\]

Each exterior angle \(= 24^\circ \)

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