A triangle has interior and exterior angles. When one side of a triangle is extended, it forms an exterior angle.
An exterior angle is the angle formed between one side of the triangle and the extension of another side.
In this lesson, we learn an important rule called the Exterior Angle Theorem.
Rule
The Exterior Angle Theorem states:
An exterior angle of a triangle is equal to the sum of the two remote interior angles.
$$\text{Exterior angle } = \text{interior angle 1} + \text{interior angle 2}$$
The remote interior angles are the two angles inside the triangle that are not next to the exterior angle.
Example
Suppose the two remote interior angles are:
\(80^\circ\) and \(30^\circ\)
Find the exterior angle.
$$\text{Exterior angle } = 80^\circ + 30^\circ$$
$$\text{Exterior angle } = 110^\circ$$
Video Explanation
Practice
Continue Learning
- Sum of Exterior Angles of a Triangle (Proof)
- Exterior Angle Theorem of a Triangle (Current lesson)
- Two Exterior Angles at a Vertex are Equal (Proof)
- Two Exterior Angles are Equal at a Vertex (Quick Proof)