Question

If the interior and exterior angle of a regular polygon
is equal. Find the number of sides of the polygon​

Answer 1

Let e be the exterior angle and i be the interior adjacent angle of a regular polygon.

The sum of exterior angle and its adjacent interior is 180  

0

, that is,

e+i=180  

0

 

Since each exterior angle is equal to its adjacent interior angle, therefore, substitute i=e

e+e=180  

0

 

⇒2e=180  

0

 

⇒e=  

2

180

​

=90  

0

 

We know that the measure of exterior angle is e=(  

n

360

​

)  

0

 where n is the number of sides of a polygon.

Here, it is given that the exterior angle is e=90  

0

, therefore,  

n=  

e

360

​

 

   =  

90

360

​

 

   =4

Hence, the number of sides is 4.