GEOMETRY

Angles In Quadrilaterals

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

1 · WHAT YOU NEED TO KNOW

The idea

Angles In Quadrilaterals questions require you to use properties and labels, not the apparent size of a drawing.

Picture itTrack the angle turn
Colourful playground markings showing shapes, equal sections, parallel lines and boundaries
2 · THE METHOD

Follow these steps

  1. Mark the information given on the diagram.
  2. Choose the relevant property or formula.
  3. Calculate one step at a time and include units.
3 · WORKED EXAMPLES

See the method in action

Example 1

A parallelogram has one interior angle of 68°. What are the other three interior angles?

Not drawn to scale68°???
  1. Adjacent angles total 180°, so 180° − 68° = 112°.
  2. Opposite angles are equal, giving 112°, 68°, 112° around the shape.
Answer: 112°, 68°, 112°
Example 2

A quadrilateral has two equal angles of 82° and a third angle of 108°. What is the fourth angle?

Not drawn to scale82°82°108°?
  1. The known total is 82° + 82° + 108° = 272°.
  2. The fourth angle is 360° − 272° = 88°.
Answer: 88°
4 · ELEVENSPRINT TIP

A useful shortcut

Never rely on a diagram being drawn to scale unless the question says it is.

5 · COMMON MISTAKES

Watch out for these

Using a remembered number without checking the shape

Name the shape or angle rule before substituting values.

6 · TRY IT YOURSELF

Three fresh questions

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