Year 6 · Summer term · Shape · Step 8
Year 6 Angles in polygons worksheets
Find the sum of the angles in a polygon and the angles of regular polygons. A free editable Word sheet with eight fluency and six reasoning questions. The answers follow the questions: the same sheet again with every answer in red.
Download the worksheets
Print on A4 portrait: every page carries the sheet twice, side by side, so you can cut down the middle and two pupils each get a half to stick in their books. Every question sits in its own box and pupils write their answers in their book. The answers follow the questions in the file: the same sheet again with every answer in red. It opens in Word, Google Docs, Pages and LibreOffice, so you can change numbers, delete questions or add your own. There is no scaffolded version of this step yet.
Not scaffolded sheet
The same questions without the extra support. For pupils working at the expected standard: eight fluency questions first, then the reasoning questions.
Sample questions from this step
These are real questions from the first set of the sheet (two from the fluency page, two from the reasoning page). Open each one to see the answer.
- The pentagon is cut into triangles by lines from corner A. The angles in a triangle add up to 180°.a) How many triangles are there? ____b) What is the sum of the angles of the pentagon? ____
Show the answer
3; 540
- All the angles of a regular polygon are equal. Work out the size of one angle of each regular polygon.a) A regular decagon ____b) A regular octagon ____c) A regular dodecagon ____
Show the answer
144; 135; 150
- This decagon is cut into 10 triangles by lines from a point in the middle.The sum of the angles of the decagon is 10 × 180 = 1,800°.Is Boba correct? Circle yes or no.Circle yes or no.Explain how you know.
Show the answer
No; The angles around the middle point (360°) are not angles of the decagon. The sum is 10 × 180 − 360 = 1,440°.
- A regular decagon and a regular quadrilateral share a side. The angle y is outside both shapes.y = ____ °
Show the answer
126
What is on each sheet
- Fluency: eight questions that start easy and get harder, with the key skill of the step practised in different ways.
- Reasoning: questions with pictures, tables and number lines (spot the mistake, true or false and explain, puzzles with one answer, an open-ended task).
- Answers in the same file: the sheet again with every answer in red, so there is only one file to download.
- Boba characters give the instructions in speech bubbles. They are decoration only.
Why one set of questions?
- Everyone works on the same content, and support comes from scaffolds instead of different, easier tasks. This follows the mastery approach described by the NCETM and the thinking in Ofsted's 2021 mathematics research review.
- Worked examples and visual representations lighten the load for pupils who need it, as the Education Endowment Foundation describes.