Exterior Angle Theorem
If one side of the triangle is created, then the exterior angle formed is equal to the sum of the two interior opposite angles. In this guide, you will learn more about the exterior angle theorem.

An exterior angle of a triangle is formed when each side of the triangle is drawn. There are \(6\) exterior angles of a triangle each of whose \(3\) sides can be extended on both sides, and \(6\) exterior angles are formed.
Related Topics
A step-by-step guide to 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 opposite (remote) interior angles of the triangle. Let’s recall some common properties of triangle angles:
- A triangle has \(3\) internal angles which always sum up to \(180\) degrees.
- It has \(6\) exterior angles and this theorem gets applied to each of the exterior angles.
Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles. Exterior angles are the angles formed between the side of the polygon and the extended adjacent side of the polygon.

Exterior Angle Theorem – Example 1:
Find the values of \(x\) and \(y\) by using the exterior angle theorem of a triangle.

Solution:
\(∠x\) is the exterior angle.
\(∠x + 92 = 180º\) (linear pair of angles)
\(∠x =\:180-92 = 88º\)
Applying the exterior angle theorem, we get, \(∠y + 41 = 88\)
\(∠y = 88-41= 47º\)
Exercises for Exterior Angle Theorem
- What is the value of \(p\) in the triangle?

- Find \(m∠YDC\).

- Find \(x\) in the given triangle and then find \(m∠ABD\).


- \(\color{blue}{60^{\circ }}\)
- \(\color{blue}{140^{\circ }}\)
- \(\color{blue}{x=5, m∠ABD = 100^{\circ }}\)
Related to This Article
More math articles
- Best Back-to-School Math Apps for Students
- Top 10 Tips You MUST Know to Retake the ASVAB Math
- How Students Can Understand Math for Free
- How To Calculate Outs In Poker
- How to Use Substitution to Solve a System of Equations: Word Problems
- What is the Type of Tangents to Circles?
- The Ultimate 7th Grade AZMerit Math Course (+FREE Worksheets)
- Full-Length 7th Grade SBAC Math Practice Test-Answers and Explanations
- Marketing Math: What’s a New Customer Really Worth?
- CLEP College Algebra-Test Day Tips
What people say about "Exterior Angle Theorem - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.