Angles in Regular Polygons for 11+ Maths: A Parent's Guide
19 October 2026
Understanding regular polygons
A regular polygon is a flat shape with all sides the same length and all angles equal. Common examples include equilateral triangles, squares, and regular pentagons. For 11+ Maths, children are expected to recognise these shapes and know how to calculate their angles.
Calculating interior angles
To find the size of one interior angle in a regular polygon, first work out the total sum of all interior angles. Use the formula: (number of sides, 2) × 180°. Then, divide this total by the number of sides. This gives the size of each interior angle.
Finding exterior angles
The sum of all exterior angles in any polygon is always 360°. For a regular polygon, divide 360° by the number of sides to find the size of one exterior angle. Remember, each interior and exterior angle at a vertex add up to 180°.
Worked examples
For a regular triangle (3 sides): (3-2) × 180° = 180°, so each angle is 180° ÷ 3 = 60°. For a square: (4-2) × 180° = 360°, so each angle is 360° ÷ 4 = 90°. For a regular pentagon: (5-2) × 180° = 540°, so each angle is 540° ÷ 5 = 108°.
Supporting your child's practice
Encourage your child to practise with different regular polygons and to check their answers using both the interior and exterior angle methods. Using diagrams and drawing the shapes can help make these calculations clearer. Regular practice with a mix of question types will build confidence for the 11+ exam.
Key insight: Understanding the relationship between the number of sides and the size of the angles helps children spot patterns and solve problems more efficiently in 11+ Maths. Practising with real examples and interactive worksheets can make this topic much easier to master.
