Year 6 · Mathematics · Space
Angle relationships
Use the facts that angles on a straight line add to 180°, angles around a point add to 360° and vertically opposite angles are equal to find unknown angles.
Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.
Learning goals
Learners will
- Classify angles by their size.
- Use angles on a straight line and angles around a point to find unknown angles.
- Recognise that vertically opposite angles are equal.
Success looks like
- I can name an angle as acute, right, obtuse, straight, reflex or a revolution.
- I can find a missing angle on a straight line.
- I can find a missing angle around a point.
- I can find vertically opposite angles when two lines cross.
The big idea
An angle measures an amount of turn. A full turn, or revolution, is 360°. A half turn is a straight angle of 180°, and a quarter turn is a right angle of 90°.
Angles are named by size:
- Acute: less than 90°
- Obtuse: between 90° and 180°
- Reflex: between 180° and 360°
Angles on a straight line add to 180°. If a straight line is split into two angles and one of them is 115°, the other must be 180° − 115° = 65°. Angles around a point add to 360°, because together they make a full turn.
When two straight lines cross, they make four angles. The angles directly opposite each other are called vertically opposite angles, and they are always equal. Neighbouring angles sit on a straight line, so each neighbouring pair adds to 180°.
These facts let you find angles without a protractor. Always show your reasoning, for example: “angles on a straight line add to 180°”.
Worked examples
Angles on a straight line
Two angles sit side by side on a straight line. One is 115°. Find the other.
- Angles on a straight line add to 180°.
- 180° − 115° = 65°.
Answer: The other angle is 65°.
Angles around a point
Three angles meet at a point. Two of them are 90° and 140°. Find the third angle.
- Angles around a point add to 360°.
- Add the known angles: 90° + 140° = 230°.
- 360° − 230° = 130°.
Answer: The third angle is 130°.
Crossing lines
Two straight lines cross. One of the angles formed is 48°. Find the other three angles.
- The angle vertically opposite the 48° angle is also 48°.
- The angle next to the 48° angle is on a straight line with it, so it is 180° − 48° = 132°.
- The angle opposite that one is also 132°.
- Check: 48° + 132° + 48° + 132° = 360°.
Answer: The angles are 48°, 132°, 48° and 132°.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
Angles on a straight line add to how many degrees?
180° — A straight line is a half turn, which is 180°.
What type of angle measures 125°?
Obtuse — 125° is greater than 90° and less than 180°, so it is obtuse.
Two angles sit side by side on a straight line. One of them is 72°. What is the other angle?
108° — Angles on a straight line add to 180°, so 180° − 72° = 108°.
Three angles meet at a point. Two of them are 100° and 120°. What is the third angle?
140° — Angles around a point add to 360°. 100° + 120° = 220°, and 360° − 220° = 140°.
Two straight lines cross and one of the angles is 35°. How many degrees is the angle vertically opposite it?
35° — Vertically opposite angles are equal, so it is also 35°.
Two straight lines cross and one of the angles is 35°. How many degrees is each angle next to it?
145° — A neighbouring angle sits on a straight line with the 35° angle, so it is 180° − 35° = 145°.
How many degrees are in a right angle?
90° — A right angle is a quarter turn: 360° ÷ 4 = 90°.
At exactly 6:00 on an analogue clock, how many degrees apart are the hour hand and the minute hand (measuring the smaller angle)?
180° — At 6:00 the hands point in opposite directions, making a straight angle of 180°.
Watch out for
- Thinking that an angle with longer arms is bigger. The size of an angle depends on the amount of turn, not the length of the lines.
- Assuming neighbouring angles at a crossing are equal. Only vertically opposite angles are equal; neighbouring angles add to 180°.
- Reading the wrong scale on a protractor. Always start counting from the 0 that sits on one arm of the angle.
Tips for parents
- Use two pencils crossed on the table to show vertically opposite angles, then rotate one pencil and watch the angle pairs stay equal.
- Ask the learner to say the angle fact they are using each time, such as “angles around a point make 360°”.
- Spot angles around the house, such as an open door, scissors or the hands of a clock, and estimate their size.
Go further
- Draw two crossing lines, measure all four angles with a protractor and check that the vertically opposite angles are equal.
- Cut a paper triangle, tear off its three corners and line them up along a straight edge. What do you notice about the total?
- Design a geometric artwork with lines crossing at different points and label as many angles as you can work out from just one measurement.