SOLUTION: Given that the sum of the interior angles of a regular polygon is four times the sum of its exterior angles. Find the number of sides of this regular polygon.

Algebra ->  Polygons -> SOLUTION: Given that the sum of the interior angles of a regular polygon is four times the sum of its exterior angles. Find the number of sides of this regular polygon.      Log On


   

Question 42202: Given that the sum of the interior angles of a regular polygon is four times

the sum of its exterior angles.

Find the number of sides of this regular polygon.
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let each interior angle of the regular polygon = x%5Eo.
Then, each exterior angle = %28180-x%29%5Eo.

Let the no. of sides = n.
Then sum of all interior angles = nx%5Eo and that of all exterior angles = n%28180-x%29%5Eo.

Given: sum of all interior angles = 4 x (sum of all exteriors)
So, nx+=+4n%28180-x%29
or x+=+4%2A180+-+4x
or 5x+=+720
or x+=+720%2F5 = 144

Thus each interior angle = 144%5Eo and each exterior angle = %28180-144%29%5Eo+=+36%5Eo.

We know that the sum of all the exterior angles of a regular polygon is 360%5Eo.

Therefore, n%2A36=360
or n=360%2F36
or n = 10

So the reqd. no. of sides of the regular polygon is 10.