Master

Exterior Angle Inequality

Master exterior angle inequality with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Exterior Angle Inequality

Study Guide

Key Definition

The exterior angle inequality theorem states that an exterior angle of a triangle is greater than either of the non-adjacent interior angles.

Important Notes

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles: $m \angle 4 = m \angle 1 + m \angle 2$
Each triangle has three exterior angles (one at each vertex), though including both linear pairs yields six.
The sum of interior angles in a triangle is always $180^\circ$.
Exterior and adjacent angles are supplementary.
The exterior angle inequality is a fundamental concept in triangle geometry.

Mathematical Notation

$\angle$ represents an angle

$\triangle$ represents a triangle

$+$ represents addition

$=$ represents equality

Remember to use proper notation when solving problems

Why It Works

The theorem holds because the sum of the measures of the non-adjacent interior angles is always less than the sum of the interior angle and its adjacent exterior angle, which is $180^\circ$.

Remember

An exterior angle is always equal to the sum of the opposite interior angles: $m \angle 4 = m \angle 1 + m \angle 2$

Quick Reference

Exterior Angle Theorem:$m \angle 4 = m \angle 1 + m \angle 2$

Understanding Exterior Angle Inequality

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

An exterior angle of a triangle is always greater than each of the non-adjacent interior angles.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

In $\triangle ABC$, if $m \angle A = 50^\circ$ and $m \angle B = 60^\circ$, what is $m \angle D$ where $\angle D$ is the exterior angle at $\angle C$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a triangular garden. The angles $\angle A$ and $\angle B$ are $45^\circ$ and $60^\circ$ respectively. Calculate the exterior angle at $\angle C$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider a triangle with angles $\angle X$, $\angle Y$, and $\angle Z$. If $\angle Z$ is the largest angle, prove that the exterior angle at $\angle Z$ is greater than $\angle X$ and $\angle Y$.

Challenge Quiz

Single Choice Quiz

Advanced

In $\triangle DEF$, if $m \angle D = 40^\circ$ and $m \angle E = 55^\circ$, which is the measure of the exterior angle at $\angle F$?

Recap

Watch & Learn

Review key concepts and takeaways