GEOMETRY

Angles Around A Point

Learn the reliable method for angles around a point, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Angles around a point total 360°.

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

Follow these steps

  1. Add all known angles around the point.
  2. Represent equal unknown angles consistently.
  3. Subtract from 360° and divide if more than one equal angle remains.
3 · WORKED EXAMPLES

See the method in action

Example 1

The smaller angle is labelled. What is the reflex angle between the same two rays?

Not drawn to scale138°reflex angle ?O
  1. The two angles made by the rays complete a full turn.
  2. Therefore the reflex angle is 360° − 138° = 222°.
Answer: 222°
Example 2

The smaller angle is labelled. What is the reflex angle between the same two rays?

Not drawn to scale138°reflex angle ?O
  1. The two angles made by the rays complete a full turn.
  2. Therefore the reflex angle is 360° − 138° = 222°.
Answer: 222°
4 · ELEVENSPRINT TIP

A useful shortcut

Subtract from 360° and divide if more than one equal angle remains.

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.