Mini Minds Hub · Free printable
Regular Polygon Angle Match: Free Printable Game for Year 8
- ForYear 8
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Regular Polygon Angle Match is a free printable maths game for Year 8 (ages 12 to 13). Children join each regular polygon to the size of one of its interior angles. They use the angle sum of the shape and a simple division, and there are lines on the sheet for writing out their working.
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 the child and keep page 2 for the grown-up. Black and white printing works well.
What is on the sheet
Children look at a set of regular polygons and a set of angles. Their job is to join each shape to the angle that belongs to it. To do this they work out the size of one interior angle for each polygon. They use the rule on the sheet: add up the angles, then divide by the number of sides. There are lines for writing, so they can show their working and not just guess.
A worked example
A regular polygon has 18 sides. What is the size of one interior angle?
This is our own example. It shows the method with a different shape from the ones children will meet, so they still have to do the sheet themselves.
Method 1: angle sum, then divide- Find the angle sum with (n minus 2) x 180. Here n is 18, so 18 minus 2 = 16.
- Work out 16 x 180. Ten lots of 180 is 1800. Six lots of 180 is 1080. The total is 2880 degrees.
- All the angles in a regular polygon are equal, so divide by the number of sides: 2880 divided by 18 = 160.
- The exterior angles of a regular polygon add up to 360 degrees. Divide by the number of sides: 360 divided by 18 = 20 degrees.
- An interior angle and its exterior angle sit on a straight line, so they add up to 180 degrees.
- 180 minus 20 = 160. This matches Method 1.
Ways to think about a regular polygon angle
Split into triangles
Pick one corner of a polygon and draw lines to every other corner it does not already touch. The shape splits into triangles. Every triangle has angles that add up to 180 degrees. This is where the angle sum rule comes from.
Find the angle sum
The number of triangles is always two fewer than the number of sides. Multiply that number by 180 to get the total of all the interior angles. Write each step on the lines so it is easy to check.
Share the total equally
Regular means every angle is the same size. So the total can be shared equally between the corners. Divide the angle sum by the number of sides to get one angle.
Check it makes sense
Each interior angle in a regular polygon is less than 180 degrees. Ask whether your answer looks sensible. Compare two shapes: does the one with more sides have a bigger or smaller angle?
Why regular polygons are worth knowing
A polygon is a flat shape with straight sides. A regular polygon has sides that are all the same length and angles that are all the same size. That equality is what makes the angle rule work. If the angles were different, dividing the total equally between the corners would not give the right answer for each one.
Regular polygons appear in tiling patterns, nuts and bolts, honeycomb, road signs and board games. Year 8 students move from knowing the names of shapes to explaining why their angles behave as they do. Matching shapes to angles is a good way to practise this, because each match needs a method and not just recall.
Skills and curriculum link
- Interior angles
- Angle sum of polygons
- Regular polygons
- Substituting into a rule
- Dividing accurately
- Showing working
Ideas that help with polygon angles
- Angles in a triangleThe three angles in any triangle add up to 180 degrees. Every polygon angle sum is built from this fact.
- Regular means equalIn a regular polygon all sides are equal and all angles are equal. This lets you share the angle sum equally.
- Interior and exteriorAn interior angle is inside the shape at a corner. An exterior angle is found by extending one side past the corner.
- Number of sidesA polygon has the same number of corners as sides. Counting carefully at the start avoids mistakes later.
Key words
- PolygonA flat shape with straight sides that is closed.
- RegularHaving all sides equal and all angles equal.
- Interior angleAn angle inside a shape, at one of its corners.
- Angle sumThe total of all the interior angles in a shape.
- VertexA corner of a shape. More than one are called vertices.
- DegreesThe unit used to measure the size of an angle.
How to use it
- Print both pages. Page 1 is for the child. Keep page 2, which has notes, help and a stretch idea.
- Read the rule on the sheet together: add up the angles, then divide by the number of sides.
- Work through the first match together. Ask the child to say why they chose that shape and angle.
- Let them carry on alone, writing their working on the lines. Then check against the notes on page 2.
- Come back another day and redo any matches that felt tricky. Repeating a familiar activity builds confidence.
Help, stretch and game ideas
If it feels too hard
Start with the shapes you already know, like the square. Work out its angle using the rule, then check it against what you know. Then move on to a shape with more sides, one at a time. Write each step on the lines.
To stretch confident children
Work out the angle sum of each shape using (n minus 2) x 180 before dividing. Then explain in a sentence why the angle sum goes up by the same amount each time a side is added.
Make it a game
Draw one of the shapes with a protractor. Take turns choosing a polygon and drawing one corner at the angle you worked out. Your partner measures it. If it matches, you score a point. Play a few rounds.
Talk about it
- How did you decide which angle belonged to which shape?
- Why do we divide by the number of sides?
- What do you notice about the angles as the shapes get more sides?
- Could you work out an angle for a shape that is not on the sheet? How?
- Where have you seen regular polygons outside of maths?
- What would go wrong if a polygon was not regular?
Take it off the page
Polygon hunt
Look around the house, street or school for regular shapes. Sketch them and count the sides. Then work out what one interior angle should be.
Paper folding
Fold and cut a strip of paper into equal parts to make a regular shape. Check the corners against a protractor.
Tile design
Draw a repeating pattern using squares and other regular shapes. Talk about which shapes fit together without gaps and why.
Who it is for
Parents
Sit beside your child for the first match, then let them lead. Ask them to explain each choice out loud. If they get stuck, suggest drawing the shape and counting the sides again.
Teachers
Use it as a starter or plenary after teaching angles in polygons, as an early finisher task or as a supply resource. The working lines make it easy to see who is using the method and who is guessing.
Home educators
Print it as part of a wider maths plan. It pairs well with a protractor, squared paper and everyday shape hunts. It is free to print again for brothers, sisters or revision a few weeks later.
Where this fits in maths
Before this sheet, children learn the names of polygons and the fact that the angles in a triangle add up to 180 degrees. They also meet angles on a straight line and in a quadrilateral. These ideas are the foundation for the polygon angle sum.
After this sheet, children can use the same reasoning to solve problems with unknown angles, tessellation and exterior angles. Later at Key Stage 4 they meet more formal geometric proof. Being able to explain a method clearly is the skill that carries forward.
Questions parents and teachers ask
- What age is Regular Polygon Angle Match for?
It is written for Year 8 (ages 12 to 13), in Key Stage 3. It also works for confident Year 7 students and as revision for older children who want to practise polygon angles.
- What will children practise?
Children find the size of one interior angle in regular polygons, in line with Key Stage 3 geometry on polygons. They also practise matching, substituting into a rule and writing out their working.
- How do I use it?
Print both pages and give page 1 to the child. They use the rule on the sheet: add up the angles, then divide by the number of sides. Check against the notes on page 2.
- What if it feels too hard?
Start with a shape you already know, like the square. Work out its angle with the rule and see that it matches what you expect. Then try shapes with more sides one at a time.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision, and it prints well in black and white on plain A4 paper.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 gives support and stretch ideas for mixed ability groups.
- Is this a screen free activity?
Yes. It is a screen free printable that needs only paper and a pencil. It works well for quiet time, rainy days and school holidays, and it encourages children to write out their thinking by hand.
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.