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

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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:

\[180 \times 3 = 540^\circ\]

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:

\((n - 2) \times 180^\circ\) (where \(n\) is the number of sides)

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

Using \((n - 2) \times 180^\circ\) where \(n\) is the number of sides:

\[(8 - 2) \times 180 = 1,080^\circ\]

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

\[\text{interior angle of a polygon} = \text{sum of interior angles} \div \text{number of sides}\]

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

The sum of interior angles is \((6 - 2) \times 180 = 720^\circ\).

One interior angle is \(720 \div 6 = 120^\circ\).

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:

\[\text{exterior angle of a polygon} = 360 \div \text{number of sides}\]

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 \(360 \div 5 = 72^\circ\).

The interior and exterior angles add up to 180°.

The interior angle is \(180 - 72 = 108^\circ\).

**Method 2**The sum of interior angles is \((5 - 2) \times 180 = 540^\circ\).

The interior angle is \(540 \div 5 = 108^\circ\).

The interior and exterior angles add up to 180°.

The exterior angle is \(180 - 108 = 72^\circ\).

- 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 \((n - 2) \times 180^\circ\) where \(n\) 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.