SOLUTION: What is the ratio of the sum of the interior angles of a pentagon and a decagon

Question 1119546: What is the ratio of the sum of the interior angles of a pentagon and a decagon
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the sum of the interior angles of a regular polygon is (n-2) * 180

for example:

a triangle has 3 sides and the sum of the angles of the triangle is equal to (3-2) * 180 = 1 * 180 = 180.

a quadrilateral has 4 des and the sum of the angles of a quadrilateral is equal to (4-2) * 180 = 2 * 180 = 360.

a pentagon is 5 sides.
a decagon is 10 sides.

the sum of the interior angles of the pentagon is 3 * 180.
the sum of the interior angles of the decagon is 8 * 180.

the ratio of the sum of the interior angles of a pentagon to the sum of the interior angles of a decagon is (3 * 180) / (8 * 180).

this results in 3/8.

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