Angles in polygons – Year 8 maths lesson
Lesson 13 of 35 in the Year 8 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 8 (ages 12–13) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 8 (ages 12–13)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why do the exterior angles of any polygon add up to 360°?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using n × 180° for the sum of interior angles. Split it into triangles from one corner: n − 2 of them.
- Thinking exterior angles depend on the number of sides. They always add up to 360°: one full turn.
Tip for home: Spot polygons in tiles and floor patterns and work out their angles.
What your child will learn
We are learning to find interior and exterior angles of polygons.
Success looks like
- I can find the sum of interior angles.
- I can use exterior angles.
- I can solve problems with regular polygons.
Key words
- polygon
- a flat shape with straight sides
- interior angle
- an angle inside the shape
- exterior angle
- the turn at each corner
- regular
- all sides and angles equal
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Walk around a polygon drawn on the floor, turning at each corner: you turn one full circle.
The big ideas (for the adult)
The interior angles of a polygon with n sides add up to (n − 2) × 180°, because it splits into n − 2 triangles.
The exterior angles of any polygon add up to 360°.
In a regular polygon all the angles are equal: each exterior angle is 360° ÷ n, and interior + exterior = 180°.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 8 maths lessons
- Ordering numbers, decimals and negatives
- Calculating with negative numbers
- Prime factors, HCF and LCM
- Rounding and estimation
- Powers and roots
- Written methods with decimals
- BIDMAS: order of operations
- Calculating with fractions
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Angle facts and parallel lines
- Transformations
- Quadrilaterals and symmetry
- Constructions and loci
- Averages and range
- Scatter graphs and correlation
- Probability
- Relative frequency and expected outcomes
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- One quantity as a fraction or percentage of another
- Percentages
- Direct and inverse proportion
- Speed, density and pressure
- Best buys and exchange rates
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 8: “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 polygons”
GCSE subject content G3: “apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.