Question

determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5

Answer 1

Answer:

Step-by-step explanation:

The sum of one exterior angle and one+interior angle is 180 since they form a linear pair.  

Let the exterior angle be x.  

angles are in ratio 1%3A5; so, the interior angle is 5x.  

Now

x+%2B+5x+=+180

6x+=+180

 

x=30...the exterior angle is equal to 30  

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

So,we multiply the exterior angle by the number of the sides.  

n+%2A+x+=+360 where n is the no. of sides  

n+%2A+30+=+360+  

+n+=+360%2F30  

n=12

hope this helps

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