Last Updated: Wednesday, July 22, 2020

Angles and properties of regular polygons – third and fourth level

What is this?

Below you will find some ideas to support you to design an activity on regular polygons which you can use or adapt for learners in your class while they are working remotely. This learning activity is based on third level experiences and outcomes.

Curriculum for Excellence (CfE) experiences and outcomes: Third level

  • I can name angles and find their sizes using my knowledge of the properties of a range of 2D shapes and the angle properties associated with intersecting and parallel lines. MNU 3-17a

Purpose of the activity

Understanding and applying links between mathematical concepts is an important skill to develop in numeracy and mathematics. Encouraging young people to think about the links between regular polygons and their angle properties will help them to develop this skill. An important skill will be for them to share their ideas and thinking with someone in their household. This could be an adult or older sibling.

Learning activities

When designing learning activities, think about the range of learners in your class and their individual circumstances. Consider the following learning activity that could be adapted for your learners:

This BBC Bitesize resource How to identify different polygons provides a useful reminder about polygons.

Part 1

Follow the steps below to calculate angle properties of regular polygons.

  • Split the regular polygon into identical (congruent) triangles.
  • What type of triangle have you created?
  • Calculate the size of angle AOB.
  • Using that value and the properties of a triangle calculate the size of angle ABO.
  • What is the size of angle OBC?
  • What is the size of interior angle ABC?
  • What is the size of exterior angle CBD?

Part 2

  • Repeat the steps above for the three regular polygons below.

  • Complete the table below to help you organise your answers.
  • Can you can spot a pattern or rule to help you fill in the table for the octagon and decagon?


Regular polygon

Number of sides (n)

Angle at centre (∠AOB)

Interior angle (∠ABC)

Exterior angle (∠CBD)

Equilateral Triangle






























Part 3

  • What do the exterior angles of a polygon add up to?
  • Can you write down a general formula for finding the exterior angle of an n-sided regular polygon?
  • Can you write down a general formula for finding the interior angle of an n-sided regular polygon?
  • Do your formulas work for the regular polygons above?
  • Use your formulas to find the size of the interior and exterior of a nonagon, dodecagon and a hexadecagon.

National Benchmarks

Depending on a young person’s individual stage of development and their prior learning, they will be working towards these National Benchmarks, by the end of third level.

Third Level

  • Names angles using mathematical notation, for example, ∠ABC.
  • Uses the angle properties of triangles and quadrilaterals to find missing angles.

Possible approach to assessing learning

Receiving examples of learning at home from young people will help you understand how they are managing the tasks you have set and provide some feedback. Using whichever approaches your school uses to communicate with young people, some of the following may be useful in supporting you to assess and celebrate their progress:

  • Young people may want to upload photos, video or comments to their online learning journal. In this case, you could encourage them to share their thinking or solutions.
  • You could encourage young people to share how they found this task. How easily did they manage? Was there anything that challenged them?
  • Depending on your platform for home learning, there may be opportunities for young people to discuss and collaborate on this task.