Octagon Angle
Octagon has eight sides and consist of eight angles. It has both interior and exterior angles. Angles inside the octagon are interior angles of octagon. Similarly, the angles at the exterior side of the octagon are termes as exterior angles. In an octagon, there are 8 interior and 8 exterior angles.
Interior Angles of Octagon
To find the measurement of each interior angle of any polygon, you can use formula
Interior angle = [(n-2) x 180] / n
For an octagon, n=8
Substituting this value into the formula:
Interior angle = [ ( 8-2 ) x 180 ] / 8
so, each interior angle of a regular octagon measure up to 135o.
The Sum of all the interior angle of an octagon, whether regular or irregular, is always 1080o.
Read More, Sum of Interior Angles of a Polygon
Exterior angle of an Octagon
To find the measurement of each exterior angle, you can use the formula:
Exterior angle = 360/n
For an octagon, n=8
Substituting this value into the formula :
Exterior angle = 360/8 = 45o
so, each exterior angle of a regular octagon measure up to 45o.
Types of Octagon
Depending on the sides, angles and vertices, an octagon is classified into the following categories:
- Regular and Irregular Octagon
- Concave and Convex Octagon
Regular Octagon : Octagon which has eight equal sides and eight equal angles, all the sides are equal in length, eight interior angle are measured to 135o and exterior angle of 45o each can be termed as regular octagon.
Irregular Octagon : Octagon which does not have all sides equal or all angles equal or we can also say whose sides and angles are not congruent is an irregular octagon. Even though its sides and angle are not equal but the sum of interior angles is always 1080o . Irregular octagon can be either convex or concave .
Concave Octagon : Octagon in which one of the angles is pointing inward and whose angle is greater than 180o are known as Concave Octagon.
Convex Octagon : Octagon which has all its interior angles less than 180o and all of its angles is pointing outward are called Convex Octagon.
Also Check, Convex Polygon
Octagon
Octagon is an eight-sided two-dimensional geometrical figure. An octagon consists of 8 interior angles and 8 exterior angles. The octagon has many interesting properties that make it a unique shape. The sum of its exterior angle is 360o and the sum of its interior angle is 1080o. There are 20 diagonals in an octagon.
In this article, we will learn the meaning and definitions of the octagon, its types, properties, area and perimeter of an octagon, and angles of an octagon, with some solved examples.
Table of Content
- What is Octagon?
- Octagon Angle
- Octagon Formula
- Octagonal Line of Symmetry
- How to Draw an Octagon
- Applications of Octagon