SOLUTION: The measure of an interior angle of a regular polygon is 144 degrees.find the apothem if half of one side of the polygon measures 5in.

Question 1008892: The measure of an interior angle of a regular polygon is 144 degrees.find the apothem if half of one side of the polygon measures 5in.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
This is a decagon, whose interior angles are 36 degrees each.
Hard to draw the triangle here, but to determine the length of the apothem, you need the leg of a right triangle whose other leg is 2.5 in and has angles of 18 and 72 degrees.
Call the apothem, a. Then we have
a/2.5 = tan 72
a = 2.5 tan 72 = 7.69 inches
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