Angles
Angles on a straight line
Angles that sit side by side on a straight line always add to 180°. Know one and you can work out the other.
A straight line is 180°
A straight line is a HALF TURN, which is 180°. So when angles sit next to each other along a straight line, they must add up to 180° exactly. If one angle is 120°, the other must be 180 − 120 = 60°.
Angles around a point
Turn all the way round and you have turned 360°. So angles that meet at a point add to 360°. If three angles at a point are 150°, 120° and one unknown, the unknown is 360 − 150 − 120 = 90°.
Which total do I use?
Look at what the angles sit on. Side by side along a STRAIGHT LINE → they add to 180°. All the way round a POINT → they add to 360°. Getting these two mixed up is the commonest error in this topic. Check whether the arms form a straight line before you choose.
More than two angles
The rule does not change when there are three or more. If 40°, 70° and one unknown angle sit on a straight line: 40 + 70 = 110 180 − 110 = 70° Add up everything you know, then subtract from 180 or 360.
Worked examples
One angle on a straight line
- Two angles sit on a straight line and one is 120°.
- They must total 180°.
- 180 − 120 = 60.
Answer: The other angle is 60°
Three angles on a straight line
- The angles are 40°, 70° and one unknown.
- 40 + 70 = 110.
- 180 − 110 = 70.
Answer: The unknown angle is 70°
Angles around a point
- Three angles meet at a point: 150°, 120° and one unknown.
- They must total 360°.
- 360 − 270 = 90.
Answer: The unknown angle is 90°
Two equal angles on a line
- Two equal angles sit on a straight line.
- Together they make 180°.
- So each is 180 ÷ 2.
Answer: Each angle is 90°
Spotting which rule to use
- Look at whether the arms make a straight line or a full turn.
- Straight line means 180°; all the way round means 360°.
Answer: Check the picture before choosing
Where you see this in real life
- A folding ruler opened flat makes 180° — a straight line.
- Slices of a pizza meet at the centre and always total 360°.
- A seesaw balanced level makes two angles that add to a straight line.
Key words
- Straight line
- A half turn, measuring 180°.
- Full turn
- A complete rotation, measuring 360°.
- Angles at a point
- Angles meeting at the same point, totalling 360°.
- Degree (°)
- The unit angles are measured in.
- Right angle
- An angle of exactly 90°.
- Sum
- The total when you add.