Understanding Angles in Regular Polygons for 11+ Maths
21 October 2026
Understanding angles in regular polygons
Regular polygons have sides and angles that are all equal. Common examples include equilateral triangles, squares, pentagons and hexagons.
For the 11+ maths exam, children are often asked to calculate the size of an interior or exterior angle in these shapes.
How to work out an interior angle
The sum of the interior angles in a polygon is found using the formula: (number of sides - 2) × 180.
To find one interior angle in a regular polygon, divide the total by the number of sides.
Key insight: Interior and exterior angles
Every interior angle and exterior angle in a regular polygon add up to 180 degrees. Exterior angles always add up to 360 degrees, no matter how many sides the polygon has.
Worked example
Find the size of one interior angle in a regular hexagon.
A hexagon has 6 sides.
Step 1: (6 - 2) × 180 = 4 × 180 = 720. This is the total of all interior angles.
Step 2: 720 ÷ 6 = 120. Each interior angle is 120 degrees.
Supporting your child at home
Encourage your child to practise with different polygons, using the formula each time.
Ask them to check their answers by adding up all the angles and seeing if they match the total given by the formula.
This helps build confidence and fluency with angle questions for the 11+ exam.
