Mini Minds Hub · Free printable
The Missing Angle Files: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
The Missing Angle Files is a free printable maths worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Children work as detectives. They find each missing angle, then use the code to unlock a letter of the suspect's name. It needs only a pencil, and page 2 gives the grown up notes, help, a stretch idea and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children work through a set of cases. Some show a straight line with one unknown angle called x. Some show angles around a point. Others show two lines crossing, where one angle is given and children find the angle opposite it or next to it. Each answer points to a letter in the code. The letters build the suspect's name.
- Straight line: 145° and x. Find x.
- Two lines cross. One angle is 110°. Find the angle opposite it.
- Around a point: 150°, 90°, 48° and x. Find x.
- Two lines cross. One angle is 55°. Find the angle next to it.
- Straight line: 40°, 30° and x. Find x.
- Around a point: 100°, 120°, 92° and x. Find x.
- Two lines cross. One angle is 116°. Find the angle next to it.
- Two lines cross. One angle is 35°. Find the angle next to it.
- Around a point: 130°, 60°, 80° and x. Find x.
A worked example
Straight line: 62°, 47° and x. Find x.
This is a different question from the ones on the sheet. It shows two ways to work.
Method 1: subtract from the total- Write 180° at the top, because angles on a straight line add up to 180°.
- Add the angles you know: 62° + 47° = 109°.
- Take that from the total: 180° − 109° = 71°.
- Add the angles you know to get 109°.
- Count on from 109° to 110°. That is 1°.
- Count on from 110° to 180°. That is 70°. Add the two jumps: 1° + 70° = 71°.
How the detective code works
Find the angle
Each case gives a clue as a sketch or a short description. Children decide which angle rule applies, then work out the missing angle.
Write it down
Children write the angle in the space provided. Writing the sum or the rule next to it makes mistakes easier to spot.
Use the code
Each angle matches a letter in the code. Children find the letter and add it to the suspect line.
Check the name
If the finished letters make a sensible name, that is a good sign. If one looks odd, go back and recheck that case.
Angle rules in a nutshell
Angles measure turn, and we measure them in degrees. A full turn is 360°. A straight line is half a turn, so angles on a straight line add up to 180°. Angles that meet at a point and fill the whole space around it add up to 360°. These two totals are the key to most missing angle questions.
When two straight lines cross, they make four angles. Angles directly opposite each other are equal. These are called vertically opposite angles. Angles side by side along one line make a straight line together. Children can use this to find any angle at a crossing from just one. Drawing a sketch makes the pattern clear.
Skills and curriculum link
- Angles on a straight line
- Angles around a point
- Vertically opposite angles
- Using a rule to find an unknown
- Subtracting from 180° and 360°
- Checking answers
Ideas that help with missing angles
- Straight lineAngles that sit together on a straight line share a total of 180°. Write that total first, then see what is left.
- Around a pointAngles that fill the space around one point share a total of 360°. Add the known angles, then find what is missing.
- Crossing linesOpposite angles at a crossing are equal. Angles next to each other along one line make 180° together.
- Check by addingPut the missing angle back with the others. If the total matches 180° or 360°, the answer fits.
Key words
- AngleThe amount of turn between two lines that meet at a point.
- DegreeThe unit for measuring angles. It is written with a small circle, like 90°.
- Straight lineA line with no bend. Angles on it add up to 180°.
- Vertically oppositeTwo angles directly across from each other where two lines cross. They are equal.
- UnknownAn angle or number we do not know yet. Here it is called x.
- Full turnA complete turn back to where you started. It is 360°.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Read the first case together. Ask your child to sketch it and decide which angle rule applies.
- Work through the cases in order. Write each angle, then find its letter in the code and add it to the suspect line.
- Check against page 2. Ask, "How did you know which total to use?" The reasoning matters as much as the answer.
- Come back another day and redo any case that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Draw a quick sketch for every case. Before you do any sums, write 180° or 360° at the top of the sketch. Add the angles you know, then subtract from the total. Do one case together, then let your child try the next alone.
To stretch confident children
Make up three new cases of your own, using any of the three types. Work out the answers, choose letters from the code, and swap with someone. Can they solve your cases and name your suspect? Ask them to explain each step.
Make it a game
Race a partner. Each of you needs a copy of page 1. The first to name the suspect with every angle correct wins. Then swap sheets and check each other's working, so a quick wrong answer cannot win.
Mistakes to watch for
Watch forA child uses 360° on a straight line, or 180° around a point.
Try thisAsk, "Is this a half turn or a full turn?" Write the total at the top of the sketch before doing any sums.
Watch forA child adds up the known angles and writes that total as the answer.
Try thisThe known angles are only part of the total. Ask what is left, then check by adding all the angles together.
Watch forA child thinks the angle next to a given angle is equal to it.
Try thisDraw the crossing. Equal angles are across from each other. Neighbours share a line, so together they make 180°.
Talk about it
- How do you know whether this case needs 180° or 360°?
- Can you explain why opposite angles at a crossing are equal?
- Which case did you find easiest, and why?
- How could you check your answer without looking at page 2?
- What would you draw to help someone who is stuck?
- Can you make up a case where the missing angle is very small?
Take it off the page
Walk the turns
Stand up and turn on the spot. Show a quarter turn, a half turn and a full turn. Say how many degrees each one is.
Angle maker
Cut two strips of card and join them at one end with a paper fastener. Open them to show different angles. Use the strips to show angles that fit together on a straight line.
Crossing lines
Use a ruler to draw two lines that cross. Measure all four angles with a protractor. Look for the pairs that match and the pairs that add up to a straight line.
Who it is for
Parents
Sit beside your child for the first case, then let them lead. Ask them to sketch each case and say which total they are using. Praise clear reasoning, not just quick answers.
Teachers
Use it as a starter, plenary, early finisher task or homework to revisit angle rules. The code gives pupils instant feedback on each answer. Page 2 has support and stretch ideas for mixed ability groups.
Home educators
This fits well into a wider maths plan. Pair it with measuring angles with a protractor, or with spotting angles around the house. Print it again for brothers and sisters, or for revision a few weeks later.
Where this fits in maths
Children meet angles in primary school. They learn about angles at a point, on a straight line and where lines cross. At Key Stage 3 they use these rules with more confidence. They also begin to give reasons for each step, not just an answer.
These rules are the foundation for later angle work. Children go on to use them with angles in triangles, quadrilaterals and parallel lines. Being secure here makes that next stage far easier.
Questions parents and teachers ask
- What age is The Missing Angle Files for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also works as revision for older pupils who need to secure the basic angle rules before moving on to triangles and parallel lines.
- What will children practise?
They practise finding missing angles on a straight line, around a point and where two lines cross. Each answer links to a letter in the code, so children get quick feedback as they build the suspect's name.
- How do I use it?
Work through the cases in order. Write each angle, then find its letter in the code and add it to the suspect line. Do the first case together, then let your child try the rest. Check with page 2.
- What if it feels too hard?
Draw a quick sketch for every case and write 180° or 360° at the top before subtracting. Work the first case together, then ask your child to explain the next one back to you before they write anything.
- Is it too easy for Year 7?
It suits consolidation. Children meet these angle rules in primary school and use them again at Key Stage 3. For more challenge, ask them to explain each step in words or make up cases of their own.
- Does the sheet include answers?
Yes. Page 2 is for the grown up and includes the answers, along with notes on how to use the sheet, help for children who find it hard and a stretch idea.
- Is this a screen free activity?
Yes. It needs only paper and a pencil, so it works for quiet time, rainy days and school holidays. It prints well in black and white on plain A4 paper, and it is free to print for home and classroom use.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.