Angles in Shapes

There are a small number of facts that you need to know about angles in shapes. Very often picture problems require you to combine this knowledge to solve a missing angle question.

1. There are 360° in a full turn

2. The angles along a straight line are 180°.

3. Vertically opposite angles are always the same as each other

The proof for this can be seen in this video from White Rose:


4. The internal angles in a triangle always add up to 180°

The proof for this can be seen in this extract from White Rose:


So, if you know two of the angles of a triangle, you can always work out the other angle by seeing how many more need to be added to reach 180°.

There are two special types of triangle which are often used in problems where you are asked to find a missing angle.

a) Equilateral Triangles

An equilateral triangle has 3 equal sides and 3 equal internal angles. As the internal angles of a triangle must add up to 180°, then sharing this equally between 3 angles means that each angle must be 60°.

b) A right angled triangle

If you are faced with a right angled triangle, this is shown with a square in the corner - you know that this angle is 90° - the other two angles must also add up to 90° as the internal angles of a triangle always add up to 180°.

c) Isosceles Triangles

Use the knowledge that an isosceles triangle has two identical angles to help you calculate the missing angles. There is an example on this video:


5. The internal angles of a quadrilateral always add up to 360°

This video from White Rose explains another way to picture the multiplication and division of 10,100 and 1000.


Combine the rules to solve the problem

This video looks at an example of a previous SATs question in which a number of the facts from above needed to be combined to calculate missing angles.