# Exterior Angle Theorem

Exterior Angle Theorem
Go back to  'Triangles'

Some common facts about the triangle that are already known to us-

• A triangle has 3 internal angles which always add to 180 degrees.
• It is a polygon with the least number of sides (three sides).
• It has 6 external angles. Let us explore the exterior angle theorem as we scroll down. Also, there is a simulator for you to explore the exterior angle theorem, and try your hand at solving the interactive questions at the end.

## Lesson Plan

 1 What Is the Exterior Angle Theorem? 2 Important Notes on Exterior Angle Theorem 3 Challenging Question on Exterior Angle Theorem 4 Solved Examples on Exterior Angle Theorem 5 Interactive Questions on Exterior Angle Theorem

## What Is the Exterior Angle Theorem?

An exterior angle of a triangle is formed when any side of a triangle is extended. $$\angle D$$ is an exterior angle for the given triangle. Exterior Angle Theorem :

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. The remote interior angles are also termed as opposite interior angles. Why Does This Theorem Work?

Here's why, ## What Is Exterior Angle Inequality Theorem?

The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles. This condition is satisfied by all the six external angles of a triangle. ## How to Use Exterior Angle Theorem?

To use the exterior angle theorem in a triangle we first need to identify the exterior angle and then the associated two remote interior angles of the triangle.

A common mistake of considering the adjacent interior angle should be avoided.

The theorem can then be used to find the measure of an unknown angle.

### Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Example:

### Also, $$\angle C = 180^{\circ} - 110^{\circ} = 70^{\circ}$$

## Where Should We Use Exterior Angle Theorem?

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