Year 5 maths · Key Stage 2 · Geometry – properties of shapes

Year 5 angles and polygons: measuring in degrees

In Year 5 children learn that angles are measured in degrees. They estimate, measure and draw angles with a protractor, and learn that angles on a straight line total 180° and angles around a point total 360°. They use the properties of rectangles to find missing lengths and angles, decide whether polygons are regular or irregular, and recognise cubes and cuboids from drawings.

Angles in degrees and polygons, explained

An angle measures turn. A full turn is 360 degrees (360°), a half turn is 180°, a quarter turn is 90° (a right angle) and three quarters of a turn is 270°. Children already know acute angles (less than 90°) and obtuse angles (more than 90° but less than 180°), and in Year 5 they add reflex angles (more than 180° but less than 360°). The size of an angle is how far one arm has turned from the other, and it doesn’t depend on how long the arms are drawn. Children estimate first, deciding whether an angle is acute or obtuse and about how big, and compare angles by size before measuring.

Measuring and drawing with a protractor is the hands-on skill of the year. Place the centre of the protractor on the point where the two arms meet, line up one arm with the 0° line, and read round the scale that starts at 0 on that arm. Drawing works the same way in reverse: draw a baseline, mark the angle on the scale, then join the mark to the corner. Lines are measured and drawn to the nearest millimetre. A reflex angle is usually found by measuring the angle on the other side and subtracting from 360°.

Angle facts let children find missing angles without measuring. Angles that meet at a point add up to 360°, angles on a straight line add up to 180°, and other multiples of 90° (90°, 180°, 270° and 360°) are linked to quarter, half, three-quarter and full turns. A rectangle has four right angles, opposite sides that are equal and parallel, and two diagonals of equal length. Diagrams use small squares for right angles, arrows for parallel lines and dashes for equal lengths. Children use these facts to work out unknown lengths and angles: if a rectangle is 8 cm long and 3 cm wide, the opposite sides are also 8 cm and 3 cm, and if a diagonal splits one corner into two angles and one is 35°, the other must be 55°, because together they make the right angle. Finding missing angles in any triangle or quadrilateral is a Year 6 objective.

A polygon is a flat shape with straight sides. In a regular polygon all the sides are equal and all the angles are equal, like a square or an equilateral triangle. If either is not true, the polygon is irregular, so a rectangle that isn’t a square is irregular (its sides are not all equal) and so is a rhombus that isn’t a square (its angles are not all equal). Children also meet 3-D shapes drawn on flat paper, and have to recognise cubes and other cuboids and think about the edges and faces they cannot see.

Words your child will hear

Degree (°): The unit for measuring angles. A full turn is 360°.
Acute and obtuse: An acute angle is less than 90°. An obtuse angle is more than 90° and less than 180°.
Reflex angle: An angle bigger than 180° and smaller than 360°.
Protractor: The semicircular tool used to measure and draw angles.
Diagonal: A straight line joining two corners of a shape that are not next to each other.
Regular polygon: A polygon whose sides are all equal and whose angles are all equal.
Irregular polygon: A polygon that is not regular, because its sides or its angles are not all equal.

What the National Curriculum says

In Year 5, pupils should be taught to:

Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
Draw given angles, and measure them in degrees (°)
Identify: angles at a point and 1 whole turn (total 360°); angles at a point on a straight line and half a turn (total 180°); and other multiples of 90°
Use the properties of rectangles to deduce related facts and find missing lengths and angles
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Two angles of 47° and 68° sit side by side on a straight line, next to an unknown angle x. Find x and say what kind of angle it is.

Angles on a straight line make a half turn, which is 180°. So 47° + 68° + x = 180°.
Add the two known angles.
```
47 + 68 = 115
```
Take that away from 180° to find the missing angle.
```
180 − 115 = 65
```
Check by adding all three: 47 + 68 + 65 = 180. Then use estimation as a second check: 65° is less than a right angle (90°), so x is an acute angle, and in the diagram it should look smaller than a corner of a book.

x = 65°, an acute angle.

Common mistakes and how to help

Reading the wrong scale on the protractor

Most protractors have two scales, one running clockwise and one anticlockwise. A child reads from the wrong end and gives 120° for an angle that is really 60°.

What helps: Estimate first: is the angle smaller or bigger than a right angle? Then start counting from the 0° where the baseline passes, and see whether the answer fits the estimate.

Thinking an angle with longer arms is bigger

A child compares the drawn lines, not the gap between them, so the angle with the longer arms looks like the larger one.

What helps: Draw the same angle with short arms and with long arms. Use a door: it can open a small amount or a lot, whatever the size of the door.

Calling a shape regular because all its sides are equal

A rhombus looks tidy and has four equal sides, so it seems regular. But its angles are not all equal, unlike those of a square.

What helps: Always ask two questions: are all the sides equal, and are all the angles equal? Both answers must be yes. A square passes both, and a rhombus that isn’t a square passes only one.

Counting only the lines you can see on a 3-D drawing

A cube drawn on paper shows 9 lines, but the cube has 12 edges. A child counts the drawn lines, forgetting that some edges are hidden behind the shape.

What helps: Look at a real box and turn it round. Draw it, showing hidden edges as dotted lines, and count the faces, edges and corners of the real thing: a cube has 6 faces, 12 edges and 8 vertices.

How to help at home

Use the clock for turns. At 3 o’clock the hands make a right angle, at 6 o’clock a straight line, at 9 o’clock a right angle again. Ask what angle the minute hand turns in 15 minutes (90°), 30 minutes (180°) and 45 minutes (270°).
Estimate, then measure. Choose the corner of a book, an open door and the hands of a clock, and ask for a guess before measuring with a protractor. Guessing first builds the sense of size that catches reading errors.
Give turning instructions. Play robot instructions around the room: “turn 90° to the right”, “turn 180°”, “turn 270° to the left”. Include a few “which way are you facing now?” questions.
Hunt for regular and irregular polygons. Look at floor tiles, windows, signs and boxes, and ask whether each is regular. Sketch a cereal box from different viewpoints and mark which edges you can’t see.

Builds on

Year 4: Shapes, angles and symmetry

Leads on to

Year 6: Angles, circles and nets

Everything in Year 5 maths

Updated 20 October 2026.