Angles in Regular Polygons Practice
22 October 2026
Angles in regular polygons made easy
Understanding angles in regular polygons is a key part of 11+ Maths. Children need to find both interior and exterior angles, and sometimes use these to solve more complex problems.
Interior and exterior angles
A regular polygon has equal sides and equal angles. The sum of interior angles depends on how many sides the shape has. For any regular polygon, each interior angle can be found using a simple formula.
Worked example
Let's find the size of one interior angle in a regular pentagon.
Step 1: Count the number of sides. A pentagon has 5 sides.
Step 2: Use the formula for the sum of interior angles: (number of sides, 2) × 180. So, (5-2) × 180 = 3 × 180 = 540.
Step 3: Divide the sum by the number of sides to get each angle: 540 ÷ 5 = 108.
The correct answer is 108 degrees.
Key insight: In every regular polygon, the formula (n, 2) × 180 gives the total of all interior angles, where n is the number of sides. Dividing this by the number of sides gives the size of one interior angle.
Practice ideas for home
Ask your child to fill in tables with the number of sides, the sum of interior angles, the size of each interior angle, and the size of each exterior angle. Try shapes like hexagons, octagons and decagons for variety.
Applying knowledge
Once your child is confident with angle calculations, set challenges using compound shapes made from regular polygons. For example, ask them to find angles where two regular polygons meet or to spot patterns in tessellations.
