Angles in polygons | Year 6 Mathematics PDF Download

What is a Polygon?

• Polygons are 2D shapes characterized by straight sides. When polygons are regular, it means that all their sides and angles are of equal measure.
• For instance, squares and equilateral triangles are examples of regular polygons.

Working out the Sum of Internal Angles

To determine the sum of internal angles in a polygon with more than four sides, you can use a formula that applies universally for all polygons:

• Sum of internal angles = (number of sides - 2) x 180°.
• After subtracting 2 from the number of sides, you essentially find out how many triangles the polygon can be divided into from a single vertex.
• Subsequently, you multiply by 180°, which represents the sum of internal angles within a triangle.
• This formula can be adapted for various polygons by adjusting the number of sides accordingly.

Regular Polygons: Understanding Internal Angles

Pentagon

A pentagon has five sides. Using the formula, you can calculate the total of the internal angles:

• Sum of internal angles = (5 - 2) x 180°
• Therefore, for a pentagon, the sum of internal angles would be (5 - 2) x 180° = 3 x 180° = 540°.

Hexagon

Since a hexagon has 6 sides, let’s substitute that amount into the formula:

• Sum of internal angles = (6 - 2) x 180
• 720° = 4 x 180
• What would one angle be in a regular hexagon?
• 720° ÷ 6 = 120°

Heptagon

All heptagons have 7 sides, so the formula to work out the internal angles would be:

• Sum of internal angles = (7 - 2) x 180
• 900° = 5 x 180°
• What would one angle in a regular heptagon be?
• 900° ÷ 7 = 128. 57° (rounded to 2 decimal places)

Octagon

Octagons have 8 sides so again, we need to adjust the formula accordingly:

• Sum of internal angles = (8 - 2) x 180°
• 1080° = 6 x 180°
• In a regular octagon, one angle would be worth:
• 1080° ÷ 8 = 135°

Irregular polygons

In irregular polygons, the total sum of the interior angles remains constant, but the value of each individual angle varies since they are of different sizes.