A polygon shape is any geometric shape that is classified by its number of sides and is enclosed by a number of straight sides. However, a polygon is considered regular when each of its sides measures equal in length. For example, a 3sided polygon is a triangle, an 8 sided polygon is an octagon, while an 11sided polygon is called 11gon or hendecagon. The number of sides of a regular polygon can be computed with the help of interior and exterior angles.
For an Instance, A hexagon is a sixsided polygon, while a triangle is a threesided one. The internal and exterior angles, which are the inside and outside angles formed by the connecting sides of the polygon, may be used to compute the number of sides of a regular polygon.

Subtract the inside angle from 180 to get the outside angle. If the inner angle was 165, for example, subtracting that from 180 would give you 15.

Divide 360 by the angle difference and 180 degrees. 360 divided by 15 = 24, which is the number of sides of the polygon in this case.

To calculate the number of sides of the polygon, divide 360 by the amount of the exterior angle. For example, if the exterior angle is 60 degrees, then dividing 360 by 60 equals 6, which is the number of sides the polygon has.
Names of Polygons
Number of Sides of a Polygon 
Polygon Shape 
3 sided polygon 
Triangle 
4 sided polygon 
Square, Rectangle, Quadrilaterals— Parallelogram, Rhombus, Kite, Dart 
5 sided polygon 
Pentagon 
6 sided polygon 
Hexagon 
7 sided polygon 
Heptagon 
8 sided polygon 
Octagon 
9 sided polygon 
Nonagon 
10 sided polygon 
Decagon 
11 sided polygon 
Hendecagon 
12 sided polygon 
Dodecagon 
20 sided polygon 
Icosagon 
100 sided polygon 
Hectagon 
n sides (infinite number of sides) 
Ngon 
Convex and Concave Polygons
A convex polygon closes in an interior space without appearing “dented.” None of the interior angles points inward. In geometrical math, you could have a 4sided polygon that points outward in all directions, like a kite, or you could have similar four sides so two of them point inward, creating a dart. The dart is concave and the kite is convex.
Each interior angle of a convex polygon measures less than 180°. A concave polygon has a minimum of one angle greater than 180°. Imagine a bowtieshaped hexagon (6 sides). It will consist of two interior angles greater than 180°.
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Simple and Complex Polygons
Simple polygons contain no selfintersecting sides. Complex polygons, also known as selfintersecting polygons, contain sides that cross over each other. An example of a complex polygon is a classic star. Most people can sketch a star on a sheet of paper very quickly, but some people label it a pentagram, complex polygon, or selfbisecting polygon.
The family of complex starshaped polygons usually share the Greek number prefix and use the suffix gram: pentagram, hexagram, heptagram, octagram, and so on.
Degrees in Polygons: How to Find Them
A polygon is a twodimensional object that is closed and made up of three or more linked line segments. Polygons include triangles, trapezoids, and octagons, to name a few. Polygons are often classed based on the number of sides and the angles and sides’ relative sizes. Polygons can also be classed as regular or nonregular. Regular polygons have equallength sides and equaldegree angles. In regular polygons, the degrees of the angles can be calculated, but this is not necessarily the case with nonregular polygons.
The polygon’s sides are multiplied by the number of sides. The total of all the inner angle degrees is (n – 2) 180. Subtract 2 from the number of sides and multiply by 180 in this calculation). The total of degrees for an octagon, for example, is (82) 180. This adds up to 1,080.
Divide the total calculated in Step 1 by the number of sides if the polygon is regular (all sides and angles are equal). This is the degree of each of the polygon’s angles. In a normal octagon, for example, each angle has a degree of 135:1. Divide 1,080 by eight to get the answer.
To determine the exterior angle measure of a regular polygon, multiply the angle from Step 2 by 180 minus the degree. This is the degree of each polygon’s outer angle. Because the angle in this example is 135 degrees, the value of the supplementary angle is 45 degrees.
Solved Examples on a Polygon Shape
Example:
1. Find out the Interior Angle of a Regular Octagon?
Solution:
A regular octagon consists of 8 sides, thus:
Exterior Angle of an octagon =[ frac{360°}{8} = 45° ]
Interior Angle of an octagon = 180° − 45° = 135°
Or we could also use the formula to determine the interior Angle of an octagon:
Interior Angle = [ frac{(n−2) times 180° }{n} ]
= [ frac{(8−2) times 180° }{8} ]
= [ frac{6 times 180° }{8} ]
= 135°
Thus, the Interior Angle of an octagon measures 135°
Example:
2. Determine the Interior and Exterior Angles of a Regular Hexagon?
Solution:
A regular hexagon consists of 6 sides, thus:
Exterior Angle of a hexagon= [frac{360°}{6} = 60°]
Interior Angle of a hexagon = 180° − 60° = 120°
Fun Facts

Interior and exterior angles of a polygon are respectively, the inside and outside angles formed by the connecting sides of the polygon.

To be a polygon, the shape must be flat, circumscribed in space, and be created using only straight sides.

Polygons with congruent angles and sides are regular; while all others are irregular.

Polygons with all interior angles measuring less than 180° are convex

Polygon having a minimum of one interior angle greater than 180° is concave.

Simple polygons don’t cross their sides

Complex polygons have selfbisecting sides.

You can spot Polygons all around you!
Conclusion
Polygons can be studied and categorized in different ways. You can see that polygons can be regular or irregular, concave or convex, and simple or complex. When you come across an unfamiliar polygon, you can simply identify its properties and classify it correctly.