Angle facts

Looking for a way to help your key stage 3 students master angle facts in preparation for the maths GCSE? Our angle facts worksheet is the perfect tool to reinforce learners’ understanding of angles and their properties.

What's included

• Free printable PDF revision sheet of angle facts for GCSE maths
• Editable Word doc version (for subscribers) to adapt.

The sheet features an outline of basic angle properties with accompanying diagrams, including:

• angles on a straight line and around a point

• vertically opposite angles

• parallel lines, corresponding angles and alternate angles

• exterior angles

• interior angles

• angles in triangles and quadrilaterals

• angles in polygons.

How to use this resource

Use this angle factsheet as a handout or print it on A3 to display on your classroom wall. It's also perfect for GCSE maths revision. 

Looking for more like this?

If you're looking for more resources and learning materials for learning about angles, try:

• Posters on angle facts
• Matching angle facts
• Angles treasure hunt
• GCSE angle revision cards

Angle facts for GCSE maths

Angles that add up to 90° are called complementary.

Angles that can be placed together on a straight line add up to 180°. These angles are called supplementary.

When 2 lines cross each other the angles between the lines make 2 pairs of equal angles: a=d & b=c These angles are called vertically opposite.

When 2 lines are parallel to each other the angles shown are said to be allied angles. These angles will add up to 180°.

When 2 lines are parallel to each other, the angles shown are said to be corresponding and are equal to each other. They are always on the same side.

When 2 lines are parallel to each other, the angles shown are said to be alternate to each other and they are equal.

Angles on a straight line add up to 180° They are called supplementary angles.        

Angles that meet at a point add up to 360°.

Angles inside a triangle add up to 180°.        

Angles inside a quadrilateral (4 sides) add up to 360°.

To work out the sum of the angles inside a polygon (multi-sided shape) otherwise called The Internal Angles, split the shape into triangles and then multiply the number of triangles by 180° (the number of degrees in a triangle): 4 x 180° = 720°

If the shape is Regular (all the angles are the same), you can divide the total by the number of corners or sides: 720° / 6 = 120°

To calculate The External Angle, draw a straight line and take the internal angle from 180°: 180° - 120 = 60°