Exterior Angle Theorem
An exterior angle equals the sum of the two remote interior angles.
Key idea
An exterior angle equals the sum of the two remote interior angles.
In depth
An exterior angle of a triangle equals the sum of the two non-adjacent interior angles. It follows because the exterior angle plus its interior neighbour make 180°, just like the angle sum.
Worked example
If interior angles are 40° and 65°, the exterior angle at the third vertex is 105°.
Real-world uses
- Working out the turning angle at a corner of a triangular route in navigation
Common mistake
Adding the adjacent interior angle instead of the two remote ones.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Exterior Angle Theorem?
An exterior angle equals the sum of the two remote interior angles. It is a topic at the intermediate level in Geometry.
Where is Exterior Angle Theorem used in real life?
Real-world examples: Working out the turning angle at a corner of a triangular route in navigation.
What should I learn before Exterior Angle Theorem?
Make sure you are comfortable with Triangle Angle Sum, the previous topic in Geometry.
What is a common mistake with Exterior Angle Theorem?
Adding the adjacent interior angle instead of the two remote ones.
How can I practise Exterior Angle Theorem?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Exterior Angle Theorem?
Move on to Triangle Inequality next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.
- Pythagorean Theorem – In a right triangle the squares on the legs sum to the square on the hypotenuse.