Angles all the way round a point make a full turn, 360°. Add the angles you know and take the total away from 360. A small square in a corner means a right angle, 90°, even though no number is written. The diagram is not drawn to scale, so use the numbers. Equal angles marked with the same letter share what is left.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- full turn
- all the way round, 360°
- right angle
- a square corner, 90°, often marked with a small square
Worked examples
110° and ? meet at a point. Find ?.
- 1.Angles around a point add up to 360°.
- 2.360 − 110 = 250.
= 250
A right angle, 120°, 70° and ? meet at a point. Find ?.
- 1.The square means 90°. Add: 90 + 120 + 70 = 280.
- 2.360 − 280 = 80.
= 80
60° and three equal angles a meet at a point. Find a.
- 1.360 − 60 = 300 for the three equal angles.
- 2.300 ÷ 3 = 100.
= 100
For parents
Method: Stand up and turn all the way round: that is 360°.
What to say: What do the angles round a point make altogether? Have you counted the square corner?
Common mistakes:
- Measures or estimates the angle from the picture instead of using an angle fact, although the diagram is not drawn to scale.
- Uses 180° as the total instead of 360°.
- Leaves out the angle marked with a small square because it has no number written on it.
- Subtracts only one of the labelled angles and forgets another.
- Finds what the equal unknown angles make together but does not share it between them.