Question

The ratio between the exterior angle and the interior angle of a regular polygon is 1: 5. Find the number of sides of the polygon.

Answer 1

Answer:

Step-by-step explanation:

The ratio between the exterior angle and interior angle of a regular polygon is 2:3.

Each interior angle of a regular polygon =  

n

180  

o

(n−2)

​  

  where n = number of sides of polygon

Each exterior angle of a regular polygon =  

n

360  

o

 

​  

 

According to question,

n

360  

o

 

​  

:  

n

180  

o

(n−2)

​  

=2:3

=>  

(n−2)

2

​  

=  

3

2

​  

 

=>n−2=3

=>n=5

Answer 2

Answer:

 ans= 12

Step-by-step explanation:

we know the sum of exterior angle is always 360°

if number of sides of polygon is 'n'

then any of the exterior is  = 360/n

then we can write interior angle is = 180- exterior angle

                                                          =180 - 360/n

                                                          = (180n-360)/n

ratio of the exterior angle and the interior angle of a regular polygon is 1: 5

we can write 1/5=(360/n) ÷((180n-360)/n)

                        1×((180n-360)/n) = (360/n) ×5    

                             180n - 360 = 360×5

                              180n = 6×360

                               n= 12

∴ polygon is of 12 sided

i hope u undrestand