## A Polygon Shape

A polygon shape is any geometric shape which is classified by their number of sides and is enclosed by a number of straight sides. However, a polygon is considered regular when each of its sides measure equal in length. For example, a 3-sided polygon is a triangle, an 8 -sided polygon is an octagon, while an 11 sided polygon is called 11-gon or hendecagon. The number of sides of a regular polygon can be computed with the help of interior and exterior angles.

## Names of Polygons

### Convex and Concave Polygons

A convex polygon closes in an interior space without appearing "dented." None of the interior angles pointing inward. In geometrical math, you could have a 4-sided polygon which 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 bowtie-shaped 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 self-intersecting sides. Complex polygons, also known as self-intersecting 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 self-bisecting polygon.

The family of complex star-shaped polygons usually share the Greek number prefix and use the suffix -gram: pentagram, hexagram, heptagram, octagram, and so on.

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### Solved Examples on a Polygon Shape

Example:

Find out the Interior Angle of a Regular Octagon?

Solution:

A regular octagon consists of 8 sides, thus:

Exterior Angle of an octagon = 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 = (n−2) × 180° / n

= (8−2) × 180° / 8

= 6 × 180° / 8

= 135°

Thus, the Interior Angle of an octagon measures 135°

Example:

Determine the Interior and Exterior Angles of a Regular Hexagon?

Solution:

A regular hexagon consists of 6 sides, thus:

Exterior Angle of a hexagon= 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 self-bisecting 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.

1. What are the Properties of a Polygon?

Answer: The identifying properties of any polygon are the following:

A 2-dimensional shape

Closing in a space (having an interior and exterior angle)

Composed with straight sides

2. What are the Types of Polygons?

Answer: Let's take a look at the huge array of shapes that are polygons and go into detail.

**A Regular Polygon:**it consists of congruent sides and interior angles.**An Irregular Polygon:**it does not have congruent sides and interior angles.**A Convex Polygon:**it contains no interior angle greater than 180° (it consists of no inward-pointing sides).**A Concave Polygon:**it contains one interior angle greater than 180°.**A Simple Polygon:**circumscribes a single interior space (boundary) and does not contain self-bisecting sides.**Complex Polygons:**it has self-bisecting sides!

3. How Do We Calculate the Angles of a Polygon?

Answer: Add the number of sides of a polygon. The total of all the degrees of the interior angles is equivalent to (n - 2) × 180. This formula implies subtract 2 from the number of sides of a polygon and multiply by 180. For example, the sum of degrees for an octagon will be (8-2) × 180. This equals to 1,080.

In a regular polygon (sides and angles are all equal), divide the sum generated in Step 1 by the number of sides. This is the degree of each angle in a polygon. For example, the degree of each angle in a regular octagon will be 135 degrees: Divide 1,080 by 8.

Calculate the supplement of the angle from Step 2 (180 minus the degree) to identify the exterior angle of a regular polygon. This is the degree of each exterior angle on the polygon. In this instance, the angle is 135, thus 180 minus 135 equals 45 for the value of the supplementary angle.