Exterior Angle Theorem

In this lesson, we will learn

• The Exterior Angle Theorem
• How to use the Exterior Angle Theorem to solve problems
• How to prove the Exterior Angle Theorem

Exterior Angle Theorem

An exterior angle of a triangle is formed by any side of a triangle and the extension of its adjacent side.

The Exterior Angle Theorem states that

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Using the Exterior Angle Theorem to solve problems

Example :

Find the values of x and y in the following triangle.

Solution:

x + 50° = 92° (sum of opposite interior angles = exterior angle)

x = 92° – 50° = 42°

y + 92° = 180° (interior angle + adjacent exterior angle = 180°.)

y = 180° – 92° = 88°

The following video explains the Exterior Angle Theorem and how it can be used the find the angles in a triangle.

The following video shows how to use the Exterior Angle Theorem to solve problems involving angles in a triangle.

This video explains the exterior angle theorem of geometry. The theorem is used to work out some applications in finding angles of a triangle.

Proof of the Exterior Angles Theorem

This video provides a two column proof of the exterior angles theorem

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