A straight line is half a turn, so the angles that sit along one side of it add up to 180°. To find a missing angle, add the angles you know and take the total away from 180. The diagram is not drawn to scale, so work from the numbers, not by measuring. When two angles are marked with the same letter they are equal: share what is left between them.
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
- straight angle
- half a turn, 180°
- not drawn to scale
- the picture is a sketch, so do not measure it
Worked examples
65° and ? sit on a straight line. Find ?.
- 1.Angles on a straight line add up to 180°.
- 2.180 − 65 = 115.
= 115
40°, 75° and ? sit on a straight line. Find ?.
- 1.Add the angles you know: 40 + 75 = 115.
- 2.180 − 115 = 65.
= 65
40° and two equal angles a sit on a straight line. Find a.
- 1.180 − 40 = 140 for the two equal angles.
- 2.140 ÷ 2 = 70.
= 70
For parents
Method: Tear a paper strip along a line and fan out the angles to see they make half a turn.
What to say: What do angles on a straight line add up to? Which angles do you already know?
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 360° as the total instead of 180°.
- Thinks the angles on a straight line add up to 90°.
- 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.