GEOMETRY

Angles In Triangles

Learn the reliable method for angles in triangles, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

The interior angles of a triangle total 180°.

Picture itFit three angles into 180°
Colourful playground markings showing shapes, equal sections, parallel lines and boundaries
2 · THE METHOD

Follow these steps

  1. Identify all known interior angles.
  2. Add them.
  3. Subtract their total from 180°.
3 · WORKED EXAMPLES

See the method in action

Example 1

In triangle XYZ, angle X is 78°. Angle Y is twice angle Z. What is the size of angle Z?

XYZ78°2 × angle Z?
  1. Angles Y and Z total 180° − 78° = 102°.
  2. Since Y is twice Z, this total is three equal parts.
  3. Angle Z = 102° ÷ 3 = 34°.
Answer: 34°
Example 2

In triangle XYZ, angle X is 63°. Angle Y is twice angle Z. What is the size of angle Z?

XYZ63°2 × angle Z?
  1. Angles Y and Z total 180° − 63° = 117°.
  2. Since Y is twice Z, this total is three equal parts.
  3. Angle Z = 117° ÷ 3 = 39°.
Answer: 39°
4 · ELEVENSPRINT TIP

A useful shortcut

Subtract their total from 180°.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.