Polygons and Interior Angles
A polygon is a closed shape with straight sides, and the sum of its interior angles depends on the number of sides.
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A polygon is a closed shape with straight sides, and the sum of its interior angles depends on the number of sides.
- Interior sum is (n - 2) x 180 degrees
- Regular polygons have equal sides and angles
- Exterior angles always total 360 degrees
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Polygons and Interior Angles?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Polygons and Interior Angles. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Polygons and Interior Angles in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Polygons and Interior Angles gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Polygons and Interior Angles in detail
A polygon is a closed shape with straight sides. The sum of interior angles of an n-sided polygon is (n − 2) × 180°, so a pentagon has 540° and a hexagon has 720°. For a regular polygon, each interior angle is that sum divided by n.
The exterior angles of any polygon add up to 360°, so each exterior angle of a regular polygon is 360°/n, and interior plus exterior makes 180°. These facts help you work out the number of sides from an angle, and they explain why only certain regular shapes tile a floor without gaps.
How the interactive helps you understand Polygons and Interior Angles
Watch the shape transformation in the interactive. Use any sliders or buttons it offers to change the values and see how the shape transformation responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Polygons and Interior Angles.
Real-life uses and examples
- Spot Polygons and Interior Angles in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Polygons and Interior Angles by estimating first, then working it out step by step.
- Use Polygons and Interior Angles when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Polygons and Interior Angles.
- Memorising the steps for Polygons and Interior Angles without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Polygons and Interior Angles
What is Polygons and Interior Angles?
A polygon is a closed shape with straight sides, and the sum of its interior angles depends on the number of sides.
What are the most important points about Polygons and Interior Angles?
The main points are: Interior sum is (n - 2) x 180 degrees; Regular polygons have equal sides and angles; Exterior angles always total 360 degrees.
Why is Polygons and Interior Angles useful?
Understanding Polygons and Interior Angles gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Polygons and Interior Angles?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Polygons and Interior Angles?
Related topics in Mathematics include Symmetry, Circles and Circumference, Circle Theorems.