Triangle Angle Sum
The interior angles of every triangle add to 180°.
About this topic
The three interior angles of any triangle add up to 180°. A neat proof tears off the corners and lines them up along a straight line, or draws a line through one vertex parallel to the opposite side and uses alternate angles.
So if two angles are known, the third is 180° minus their sum. A right triangle's two acute angles total 90°, and each angle of an equilateral triangle is 60°. This fact is fundamental to the angle sum of polygons.
Worked example: a triangle has angles x, 2x and 3x. Then 6x = 180, so x = 30, and the angles are 30°, 60° and 90°, a right triangle. If two angles are 47° and 68°, the third is 180 − 115 = 65°. In an isosceles triangle with a 40° apex angle, each base angle is (180 − 40)/2 = 70°.
Surveyors use the sum to find an angle they cannot measure directly when they know the other two. On a sphere, such as the Earth, triangles can exceed 180°, so the rule belongs to flat geometry. A common mistake is adding to 360° by confusing triangles with quadrilaterals. Another is forgetting that an obtuse triangle has only one obtuse angle, since two would already exceed 180°. Always check that your three answers add up to 180 as a quick test of your arithmetic.
Key ideas
- Drag any corner and the sum stays 180°
- Find a missing angle by subtraction
- Proof uses parallel lines
Quick check
Use cases: where Triangle Angle Sum helps
- Homework: review the key idea behind Triangle Angle Sum before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Triangle Angle Sum without notes.
- Visual learning: play with the interactive lab to see how Triangle Angle Sum changes when you adjust its inputs.
- Teaching a friend: explain Triangle Angle Sum in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Triangle Angle Sum?
The interior angles of every triangle add to 180°.
What will I learn in Triangle Angle Sum?
Drag any corner and the sum stays 180°. Find a missing angle by subtraction. Proof uses parallel lines.
Is Triangle Angle Sum part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Triangle Angle Sum lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Triangle Angle Sum?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.