Polygon Angle Measurements:
1. To find the total number of degrees in any polygon, subtract two from the number of sides and multiply that number by 180.
Example: For a dodecagon, which has 12 sides, 12 - 2 = 10. 10 x 180 = 1,800 total degrees.
2. If a polygon is regular (all sides and angles are congruent), then dividing the number of sides into the total number of degrees will give you the measurement of each (congruent) angle. The formula for this is (n-2) x 180.
n
Example: For a pentagon, which has five sides, 5-2 = 3. 3 x 180 = 540.
540 = 108.
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3. The total number of external degrees in any polygon is 360 degrees. To find the measurement of any regular external angle divide 360 by n.
Example: The measure of each external angle in a regular hexagon is 60, or 360.
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