SOLUTION: in a regular 31 gon what is the measurement of each interior angle and measurement of each exterior angle

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Question 569092: in a regular 31 gon what is the measurement of each interior angle and measurement of each exterior angle
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
The exterior angle is the angle between the line extending one side and the next side. In other words, it is the angle by which you change direction as you turn a corner (vertex) as make your way around the polygon, along the perimeter. Of course, the sum of all those angles shows how much you turned yourself around on one full lap along the perimeter: 360 degrees. If the polygon was a regular 31-gon, all 31 angles were the same so the measurement of each, in degrees is

The interior angle is the angle between consecutive sides inside the polygon. It is supplementary to the exterior angle, so its measurement, in degrees, is

However, maybe your teacher expected you to memorize and use some formula in the textbook that says that the sum of the interior angles of an n-gon is

The result is the same.
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