Polygons are multi-sided shapes with different properties. Shapes have symmetrical properties and some can tessellate.

Part of

Polygons can be regular or irregular. If the angles are all equal and all the sides are equal length it is a regular polygon.

To find the sum of interior angles in a polygon divide the polygon into triangles.

The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.

Calculate the sum of interior angles in a pentagon.

A pentagon contains 3 triangles. The sum of the interior angles is:

The number of triangles in each polygon is two less than the number of sides.

The formula for calculating the sum of interior angles is:

(where is the number of sides)

- Question
Calculate the sum of interior angles in an octagon.

Using where is the number of sides:

All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is:

- Question
Calculate the size of the interior angle of a regular hexagon.

The sum of interior angles is .

One interior angle is .

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.

The sum of the exterior angles of a polygon is 360°.

The formula for calculating the size of an exterior angle is:

Remember the interior and exterior angle add up to 180°.

- Question
Calculate the size of the exterior and interior angle in a regular pentagon.

**Method 1**The sum of exterior angles is 360°.

The exterior angle is .

The interior and exterior angles add up to 180°.

The interior angle is .

**Method 2**The sum of interior angles is .

The interior angle is .

The interior and exterior angles add up to 180°.

The exterior angle is .

- The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.
- The formula for calculating the sum of interior angles is where is the number of sides.
- All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
- The sum of exterior angles of a polygon is 360°.
- The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.