# 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.