A triangle has three sides and three interior angles. When we extend the sides of a triangle, we form exterior angles.

An exterior angle is the angle formed between one side of the triangle and the extension of another side.

In this lesson, we will prove that the sum of the exterior angles of a triangle is 360°.

Rule

The sum of the exterior angles of any triangle is:

Exterior Angle 1 + Exterior Angle 2 + Exterior Angle 3 = 360°

This is the same as a full turn (a complete circle).

Proof Idea

Imagine walking around a triangle.

At each vertex, you turn to follow the next side. These turns are the exterior angles.

When you complete the walk and return to the starting point, you have made a full turn, which is 360°.

Therefore, the sum of the exterior angles of a triangle is 360°.

Example

If two exterior angles of a triangle are 120° and 100°, find the third angle.

120 + 100 + x = 360

220 + x = 360

x = 140°

So the third exterior angle is 140°.

Video Explanation

Practice

• More Examples

• Take the Quiz

Continue Learning

1. Types of Triangles
2. Triangles (Basics)
3. Sum of Angles of a Triangle is 180° (Proof)
4. Find the Missing Angle of a Triangle
5. Sum of Exterior Angles of a Triangle (Proof)
6. Exterior Angle Theorem of a Triangle
7. Two Exterior Angles at a Vertex are Equal (Proof)
8. Two Exterior Angles are Equal at a Vertex (Quick Proof)

Navigation

• Back to Triangles
• Back to Home