Angles, Lines And Polygons - Edexcel - GCSE Maths Revision - BBC

In this guide

1. Revise
2. Video
3. Test

Pages

1. Types of angle
2. Angles at a point and on a straight line
3. Angles in parallel lines
4. Triangles
5. Quadrilaterals
6. Polygons
7. Symmetry

Polygons

A polygon is a 2D shape with at least three sides.

Types of polygon

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

Interior angles of polygons

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°.

Example

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.

Show answer

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

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

Calculating the interior angles of regular polygons

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.

Show answer

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

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

Exterior angles of polygons

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°.

Calculating the exterior angles of regular polygons

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.

Show answer

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 \(180 - 108 = 72^\circ\).

Key fact

• 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.

Next pageSymmetryPrevious pageQuadrilaterals

More guides on this topic

• NEW: Angles
• NEW: Angles in parallel lines
• NEW: Polygons
• NEW: Line and rotational symmetry
• NEW: Constructing triangles
• NEW: Ruler and compass constructions
• NEW: Loci
• NEW: Bearings
• NEW: Perimeter
• NEW: Area
• NEW: Volume of a prism
• NEW: Surface area of a prism
• NEW: Pyramids, cones and spheres
• NEW: Nets, plans and elevations
• NEW: Circumference and arc length
• NEW: Area of circles and sectors
• NEW: Higher – Calculating angles using circles
• NEW: Higher – Using the alternate segment theorem, tangents and chords
• NEW: Reflection
• NEW: Rotation
• NEW: Translation
• NEW: Enlargement
• NEW: Higher − Negative enlargements
• NEW: Combined transformations and invariant points
• NEW: Congruent and similar shapes
• NEW: Higher – Similarity in 2D and 3D shapes
• NEW: Pythagoras' theorem
• NEW: Solving 2D and 3D problems using Pythagoras' theorem
• NEW: Right-angled trigonometry
• NEW: Sine rule
• Loci and constructions - Edexcel
• Circles, sectors and arcs - Edexcel
• Circle theorems - Higher - Edexcel
• Circle theorems - Higher - Edexcel
• Circle theorems - Higher - Edexcel
• Pythagoras' theorem - Edexcel
• Pythagoras' theorem - Edexcel
• Units of measure - Edexcel
• Trigonometry - Edexcel
• Vectors - Edexcel

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