Exterior Angles Of Triangle - Definition, Formula, Properties - Cuemath

Exterior Angle of Triangle

The exterior angles of a triangle are those angles that are formed outside it. In other words, the exterior angle of a triangle is the angle that is formed between one of its sides and its adjacent extended side. Let us learn more about the exterior angle of triangle in this article.

1.	What is the Exterior Angle of Triangle?
2.	Exterior Angle of Triangle Properties
3.	Exterior Angle of Triangle Formula
4.	FAQs on Exterior Angle of Triangle

What is the Exterior Angle of Triangle?

When any side of a triangle is extended, the angle that is formed with this side and its adjacent side is called the exterior angle of a triangle. There are three exterior angles in a triangle. It should be noted that each exterior angle forms a linear pair with its corresponding interior angle. We know that the interior angle of a triangle is formed inside it where the sides meet at a vertex. Observe the following figure to distinguish between the interior angles and the exterior angles of a triangle.

We can see that each interior angle forms a linear pair with its corresponding exterior angle. This means that the sum of each exterior angle and its respective interior angle is equal to 180°.

Exterior Angle of Triangle Properties

There are three basic properties of the exterior angles of a triangle.

• In a triangle, each exterior angle and its corresponding interior angle form a linear pair of angles. This means that the sum of the interior and exterior angle is equal to 180°.
• The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). This is also known as the Exterior Angle theorem.
• The sum of all the exterior angles of a triangle is 360°.

Exterior Angle of Triangle Formula

Based on the properties of the exterior angles, the following formulas can be used to find the exterior angles of a triangle. Referring to the triangle given below, the formulas can be understood in a better way.

• Each Exterior angle = 180 - Interior angle. Here, ∠e = 180 - ∠b. Similarly, ∠d = 180 - ∠c, and ∠f = 180 - ∠a
• Exterior angle = Sum of Interior opposite angles. Here, ∠d = ∠a + ∠b, ∠f = ∠b + ∠c, and ∠e = ∠a + ∠c
• Sum of the Exterior angles of a triangle = 360°. Here, ∠d + ∠e + ∠f = 360°

Related Links

Check out the links given below related to the exterior angles of a triangle.

• Interior angles
• Exterior Angles of a Polygon
• Exterior Angle Theorem
• Linear Pair of Angles