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

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Question 936025: determine the number of sides of a polygon whole exterior and interior angles are in ratio 1:5
Answer by MathLover1(20850) About Me  (Show Source):
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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