Calculating Interior Angles in Regular Polygons: Worked Example
22 October 2026
Understanding how to calculate interior angles in regular polygons is a key skill for 11+ maths. If your child can spot the pattern in shapes like pentagons or hexagons, they will find these questions much easier. Here's a clear, step-by-step example to show exactly how it works, just like you might see on maths.com uk.
Worked example
What is the size of each interior angle in a regular pentagon?
Step 1: Count the 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 find each angle: 540 ÷ 5 = 108.
Key insight: In a regular polygon, all interior angles are equal.
The correct answer is 108 degrees.
Now your child can recognise the method for finding an interior angle in any regular polygon. With this example, they'll feel ready to tackle similar questions on their own.
