Angles
Angles in a triangle
The three angles inside any triangle always add up to 180°. If you know two of the angles, you can work out the third.
The angles add up to 180°
If you tear the three corners off a triangle and put their points together, they make a straight line. A straight line is 180°, so the three angles of a triangle always add up to 180°. To find a missing angle, add the two you know and subtract the total from 180°.
Special triangles
• An equilateral triangle has three equal sides and three equal angles of 60°. • An isosceles triangle has two equal sides and two equal (base) angles. • A right-angled triangle has one right angle of 90°, shown by the ∟ symbol. Matching dashes on the sides show which sides are equal.
Combining rules
Sometimes a triangle sits on a straight line. Angles on a straight line add up to 180°, so you can find an angle on the line first, then use the triangle rule to find the others.
Worked examples
Finding the third angle
- A triangle has angles of 30° and 70°. Add them: 30° + 70° = 100°.
- The angles in a triangle add to 180°, so subtract: 180° − 100°.
Answer: The third angle is 80°.
An isosceles triangle
- An isosceles triangle has a top angle of 126° and two equal base angles.
- The base angles share what is left: 180° − 126° = 54°.
- Split 54° equally: 54° ÷ 2.
Answer: Each base angle is 27°.
An equilateral triangle
- An equilateral triangle has three equal angles.
- Share 180° equally between the three angles: 180° ÷ 3.
Answer: Each angle is 60°.
A right-angled triangle
- A right-angled triangle has a right angle of 90° and another angle of 30°.
- Add them: 90° + 30° = 120°, then subtract from 180°.
Answer: The third angle is 60°.
A triangle on a straight line
- The angle on the straight line next to the triangle is 127°.
- Angles on a straight line add up to 180°, so the inside angle is 180° − 127° = 53°.
- Now use the triangle rule with the other known angle, 84°: 84° + 53° = 137°, then 180° − 137°.
Answer: The remaining angle of the triangle is 43°.
Where you see this in real life
- Checking the angle at the top of a roof so the tiles fit.
- Working out the slope of a triangular ramp or bracket.
- Designing a triangular flag or road sign with the correct angles.
Key words
- Angle sum
- The total of the angles in a shape; for a triangle it is always 180°.
- Equilateral triangle
- A triangle with three equal sides and three equal 60° angles.
- Isosceles triangle
- A triangle with two equal sides and two equal angles.
- Scalene triangle
- A triangle with all sides and all angles different.
- Right angle
- An angle of exactly 90°, shown by the ∟ symbol.