Two angles of a triangle are given. Find the third angle.
α = 35°, β = 75°, γ = □
Answer: 70°
Year 6 Properties of Shapes Word Problems with Answers (PDF)
Imaginesis: printable Year 6 Properties of Shapes maths worksheets for England (National Curriculum) — Finding Missing Angles in Triangles and Quadrilaterals, Finding a Missing Angle in a Full Turn, Nets of solids: flat patterns that fold into 3-D shapes: word problems with hints, answers and worked solutions as PDF, also as a test in groups A–D.
Sample word problems
An angle is split into two parts. Find the missing part β.
α + β = 90°, α = 50°, β = □
Answer: 40°
Can the figure in the picture be folded into a cube? Answer yes or no.
□
Answer: yes
Objectives in this topic
Finding Missing Angles in Triangles and Quadrilaterals
Children learn to calculate a missing angle in any triangle or quadrilateral using the facts that their interior angles total 180° and 360° respectively.
KS3.GM.12 derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygonsY6.GPS.3 compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
Children learn to use the core geometric facts that the interior angles of any triangle add up to 180° and the interior angles of any quadrilateral add up to 360°. Using addition and subtraction, pupils total the known angle measurements and subtract that sum from either 180° or 360° to calculate the single remaining angle.
A frequent mistake occurs when children mix up the two whole totals, incorrectly attempting to subtract the angles of a four-sided shape from 180° instead of 360°. Arithmetic slips are also common when adding three two-digit numbers together before subtracting from 360°, especially when regrouping across zeros.
Practice tasks focus directly on calculating missing values from labelled shape diagrams. Worksheets present either The third angle of a triangle, providing two known degree measurements to find the final corner, or The fourth angle of a quadrilateral, providing three known angles to find the fourth.
Create a worksheet for this skill
Drill sheet (numbers only)
Task types: Angle sum of a polygon step by step · Angle sum of a polygon: compare · Angles of a right triangle: the other acute angle · Angles of a triangle: does such a triangle exist? · The fourth angle of a quadrilateral · The third angle of a triangle · The third angle of a triangle: choose the result · Angles of an isosceles triangle: the apex angle · Angles of a triangle in a given ratio · The third angle of a triangle in real life
Finding a Missing Angle in a Full Turn
Children learn to work out an unknown angle by recognising which angles make up a full turn (360°) or a straight line (180°) and taking the known angles away from that total.
KS3.GM.10 apply the properties of angles at a point, angles at a point on a straight line, vertically opposite anglesKS3.GM.11 understand and use the relationship between parallel lines and alternate and corresponding anglesY5.GPS.5 use the properties of rectangles to deduce related facts and find missing lengths and anglesY6.GPS.5 recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.Y5.GPS.4.a angles at a point and one whole turn (total 360°)Y5.GPS.4.b angles at a point on a straight line and ½ a turn (total 180°)
At this stage, children are expected to recognise angles that meet at a point, lie on a straight line, or are vertically opposite, and to find the missing angle in each case. The curriculum gives the totals, 360° for a full turn and 180° for a straight line. It does not set a range of sizes for the unknown angle, so the numbers on each worksheet are chosen by the task.
A common mistake is choosing the wrong total. A child may see a straight line but subtract from 360°, or treat a pair of angles on a straight line as if they made a full turn. Another frequent error is subtracting only one of the known angles, or taking the unknown away from one given angle instead of from the whole. Both errors usually come from not first deciding which whole the angles belong to.
In this Year 6 area, the printable templates for this skill include:
- Third angle in a full turn: choose the measure
- Missing part of an angle: three angles in a full turn
- Missing part of an angle: choose the measure
- Find the missing part of an angle
The first two templates are built around angles that share a full turn. The other two cover missing-part tasks more generally. Work on alternate and corresponding angles with parallel lines is listed under the key stage 3 (secondary) points, so it is not something these Year 6 templates are designed to practise.
Create a worksheet for this skill
Drill sheet (numbers only)
Task types: Find the missing part of an angle · Missing part of an angle: choose the measure · Missing part of an angle: three angles in a full turn · The third angle of a triangle step by step · The third angle of a triangle: extra data · Third angle in a full turn: choose the measure
Nets of solids: flat patterns that fold into 3-D shapes
Your child learns to tell whether a flat pattern will fold up into a 3-D shape, and to describe and build simple solids, including making nets.
Y6.GPS.2 recognise, describe and build simple 3-D shapes, including making nets
In Year 6 maths, this skill is about recognising, describing and building simple 3-D shapes, including making nets. A net is a flat pattern that folds up to make a solid. To see whether a pattern will work, your child has to picture which faces meet and which faces sit opposite each other.
A common mistake is judging a pattern by whether it looks roughly like a box. Six squares arranged in the right number of rows may still fold so that two squares land on the same face and leave another face empty. The layout of the squares matters more than how many there are.
The printable task in this area is "Net of a cube: is it a net?" Your child is shown a flat pattern and decides whether it folds into a cube, then gives a yes or no and explains why. A helpful way to check at home is to cut out the pattern, fold it, and count the faces. This is a suggestion for practice, not a separate requirement.