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.

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) (Show Source): You can put this solution on YOUR website!
Let each interior angle of the regular polygon = .
Then, each exterior angle = .

Let the no. of sides = n.
Then sum of all interior angles = and that of all exterior angles = .

Given: sum of all interior angles = 4 x (sum of all exteriors)
So,
or
or
or = 144

Thus each interior angle = and each exterior angle = .

We know that the sum of all the exterior angles of a regular polygon is .

Therefore,
or
or n = 10

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