Question

the measure of each exteriors angle of regular polygon of side 9 is​

Answer 1

• The measure of each exterior angles of a regular polygon = 40°.

Given :

• The side of a regular polynomial = 9.

To Find :

• The measure of each exterior angles of a regular polygon.

Solution :

We know that,

The sum of the exterior angles of a regular polygon is 360°.

We have to find the measure of each exterior angle of a regular polygon.

Given that,

• Side of a regular polygon is 9.

So,

We have to divide the sum of exterior angles of a regular polygon by side of a regular polygon.

I.e.,

$\green{ \boxed{ \tt{ \pink{ \dfrac{sum \: of \: exterior \: angles \: of \: a \: regular \: polygon}{side \: of \: a \: regular \: polygon} }}}}$

We have,

• Sum of exterior angles of a regular polygon = 360°.
• Side of a regular polygon = 9.

$\implies \cancel \dfrac{360 \degree}{9}$

$\implies \dfrac{40 \degree}{1}$

$\implies 40 \degree$

Hence,

The measure of each exterior angles of a regular polygon is 40°.

Verification :

Sum of all exterior angle of a polygon = 360°.

We have,

Sides of a regular polygon = 9.

Measure of each exterior angles = 40°.

So, we have to add the measure of each exterior angles.

$\implies 40 \degree + 40 \degree + 40 \degree + 40 \degree + 40 \degree + 40 \degree +40 \degree + 40 \degree + 40 \degree = 360 \degree$

We add 9 times because the given sides of a regular polygon is 9.

$\implies 80 \degree + 80 \degree + 80 \degree + 80 \degree + 40 \degree = 360 \degree$

$\implies 160 \degree + 160 \degree + 40 \degree = 360 \degree$

$\implies 320 \degree + 40 \degree = 360 \degree$

$\implies 360\degree + 360 \degree$

Hence Verified !!