Triangle Angle Sum
Interior angles of a triangle add to 180°.
Key idea
Interior angles of a triangle add to 180°.
In depth
The interior angles of any triangle add to 180°. Proof: draw a line through one vertex parallel to the opposite side; alternate angles show the three angles form a straight line.
Worked example
A triangle with angles 50° and 60° has the third angle 180 − 110 = 70°.
Formula
Real-world uses
- Finding a missing angle in a triangular plot of land or a roof gable
Common mistake
Applying it to quadrilaterals, whose angles sum to 360°.
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 Triangle Angle Sum?
Interior angles of a triangle add to 180°. It is a topic at the beginner level in Geometry.
What is the formula for Triangle Angle Sum?
The key formula is A + B + C = 180°.
Where is Triangle Angle Sum used in real life?
Real-world examples: Finding a missing angle in a triangular plot of land or a roof gable.
What should I learn before Triangle Angle Sum?
Make sure you are comfortable with Triangles: Classification, the previous topic in Geometry.
What is a common mistake with Triangle Angle Sum?
Applying it to quadrilaterals, whose angles sum to 360°.
How can I practise Triangle Angle Sum?
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 Triangle Angle Sum?
Move on to Exterior Angle Theorem next.
Related beginner topics in Geometry
- Points, Lines and Planes – The undefined building blocks of geometry.
- Line Segments and Rays – A segment has two endpoints; a ray starts at a point and goes on forever.
- Angles – Two rays sharing an endpoint; measured in degrees.
- Types of Angles – Acute <90°, right 90°, obtuse between 90° and 180°, straight 180°.
- Measuring Angles with a Protractor – Align the baseline and read the scale.
- Complementary and Supplementary – Pairs summing to 90° or 180°.