SOLUTION: hi i have a geometry investigation to do about the equation for one interior angle of a regular polygon and i put the points for the number of sides to the measure of one angle in

Question 174813: hi i have a geometry investigation to do about the equation for one interior angle of a regular polygon and i put the points for the number of sides to the measure of one angle in my calculator(3 sides=60 degrees, 5 sides= 108 degrees, etc. from 3 to 8 sides) and then went to stat calc and did the quad regression. I got an equation of y=-2.78x^2+44.93x-48.02. One of the questions is How many degrees is one interior angle of a regular 100-gon. So, i put in 100 for x but get a negative number. Please get back to me asap!
Thanks!!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The sum of the interior angles of any polygon, regular or otherwise, is given by

degrees where n is the number of sides forming the polygon. The number of interior angles in any polygon is equal to the number of sides forming the polygon.

Since you are dealing with a regular polygon of 100 sides, it has 100 equal length sides and 100 interior angles of equal measure, so to find the measure of one of the angles, calculate the sum of all of them and divide by the number of angles. In other words, evaluate:

It might be of interest to note that no matter how many sides you choose, the interior angles will always be less than 180 degrees. You might want to think about the limiting shape as the number of sides gets very large.

John

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