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Angles in a triangle
Years 5 to 9
The three angles in any triangle always add up to 180°.
For learners
Every triangle has three angles. Add them up and you always get 180°. It works for tall, thin and wide triangles.
If you know two angles, you can find the third. If two angles are 50° and 60°, the third is 180 − 50 − 60 = 70°.
Try it: tear the three corners off a paper triangle and put them side by side. They make a straight line, which is 180°.
A worked example
A triangle has angles of 35° and 85°. What is the third angle?
- 35 + 85 = 120.
- 180 − 120 = 60.
- The third angle is 60°.
For grown-ups
The paper-tearing activity is a convincing demonstration. A straight line is 180°, and the corners fit along it. Later, this fact is used to prove angle rules for polygons and parallel lines.
Common mistakes
- Using 360° (the total for a quadrilateral).
- Reading the wrong scale on a protractor.
- Forgetting that an isosceles triangle has two equal angles.
Why it matters
Triangles are the building blocks of shapes. Surveyors, builders and trigonometry all depend on this rule.
Topics in quarter that use this
- Angles
- Angles in polygons
- Angles in parallel lines
- Bearings