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Polygon Rules Help (page 2)

By — McGraw-Hill Professional
Updated on Oct 3, 2011

Positive And Negative Exterior Angles

An exterior angle of a polygon is measured counterclockwise between a specific side and the extension of a side next to it. An example is shown in Fig. 4-7. If the arc of the angle lies outside the polygon, then the resulting angle θ has a measure between, but not including, 0 and 180 degrees. The angle is positive because it is measured “positively counterclockwise”:

0° < θ < 180°

If the arc of the angle lies inside the polygon, then the angle is measured clockwise (“negatively counterclockwise”). This results in an angle φ with a measure between, but not including, −180 and 0 degrees:

−180° < φ < 0°

 

Other Plane Figures Some Rules of “Polygony” Positive And Negative Exterior Angles

Fig. 4-7 . Exterior angles of an irregular polygon. The angle θ is measured “positively counterclockwise” while the angle φ is measured “negatively counterclockwise.”

Perimeter Of Regular Polygon

Let V be a regular plane polygon having n sides of length s , and whose vertices are P 1 , P 2 , P 3 , . . ., P n as shown in Fig. 4-8. Then the perimeter, B , of the polygon is given by the following formula:

B = ns

 

 

Other Plane Figures Some Rules of “Polygony” Perimeter Of Regular Polygon

Fig. 4-8 . Perimeter and area of a regular, n -sided polygon. Vertices are labeled P 1 , P 2 , P 3 , . . ., P n . The length of each side is s units.

Practice problems for these concepts can be found at:  Other Plane Figures Practice Test.

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