How it works

The sum of exterior angles of any polygon is always 360°. The sum of interior angles of a polygon with n sides is (n-2) × 180°. For a regular polygon, each interior angle equals the total interior angle sum divided by the number of sides, and each exterior angle equals 360° divided by the number of sides. Interior and exterior angles at a vertex are supplementary.

The method

1. 1.Determine the number of sides, n
2. 2.Use (n-2) × 180° for the interior angle sum
3. 3.Use 360° ÷ n for each exterior angle of a regular polygon
4. 4.Use interior + exterior = 180° at each vertex if needed

Worked example

Find the sum of interior angles of a hexagon.

1. n = 6
2. Sum = (6-2) × 180° = 720°

Worked example

Find each interior angle of a regular pentagon.

1. Sum = (5-2) × 180° = 540°
2. Each angle = 540° ÷ 5 = 108°

Common mistakes

• Using the wrong formula for interior versus exterior angle sums
• Forgetting that exterior angles of any polygon always sum to 360°
• Not dividing by the correct number of sides for regular polygons