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The Many Facets of a Polygon
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November 2, 2016
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March 4, 2017
A Polygon is a plane figure formed by at least three sides and angles. The table below displays details of some of the common polygons.
| Name | No. of sides | No. of angles |
| Triangle | 3 | 3 |
| Quadrilaterals | 4 | 4 |
| Pentagon | 5 | 5 |
| Hexagon | 6 | 6 |
| Heptagon | 7 | 7 |
| Octagon | 8 | 8 |
| Nonagon | 9 | 9 |
| Decagon | 10 | 10 |
| n-gon | n | n |
Polygon Angles: Angles of a polygon are represented in two ways.
Interior Angles: An interior angle of a polygon is an angle formed inside the polygon by any two adjacent sides of the polygon. The sum of the interior angles of a polygon is based on the number of sides the polygon has, and it is calculated as
Sum of interior angles = (n-2) * 180o
“n” is the number of sides of a polygon
Example 1: Calculate the sum of interior angles of a pentagon.
Solution: Pentagon has 5 sides (n =5)
Sum of interior angles = (5-2) * 180o
= 3 * 180o
= 540o
Exterior angles: Angles formed between any side and extension of its adjacent side. The sum of exterior angles of a polygon is equal to 360o . The Figure below represents the exterior angles of a pentagon.
Fig 1: Exterior angles of a pentagon
Measure of angle A+B+C+D+E= 360o
Based on the length of the sides and size of the angles, polygons are classified as Regular and Irregular polygons.
Regular polygon: Each side of a polygon is equal in length, and each angle is equal in size.
Fig 2: Regular pentagon
Each angle of a regular polygon = Sum of angles of polygon/Number of sides of a polygon
Example 2: What is the measure of each interior angle of a regular octagon?
Solution: Octagon has 8 sides (n =8)
Sum of interior angles= (8 – 2) * 180o
= 6 * 180o
= 1080o
Each angle of a regular Octagon = 1080o/8
= 135o
Number of sides of a polygon: Let’s say each exterior angle of a regular polygon is xo , the number of sides of a polygon is calculated as
Number of sides = Sum of exterior angles/xo
Example 3: The measure of one of the exterior angles of a polygon is 20o . Number of sides of a polygon is?
Solution: Number of sides = Sum of exterior angles/20o
= 360o/ 20o
= 18
Therefore, the given polygon has 18 sides.
Irregular polygon: Each side and angle of a polygon is unequal in length and size. Example
Fig 3: irregular pentagon
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