There are a limited number of facts that you need to know in order to solve problems involving angles in shapes. Very often, picture problems require you to combine these pieces of knowledge to solve 'missing angles' questions.
1. There are 360° in a full turn
2. The angles along a straight line always add up to 180°
3. Vertically opposite angles are always the same as each other
The proof for 3. can be seen in this White Rose video.
4. The internal angles of a triangle always add up to 180°
Look at this video to see the proof for this statement.
So, if you know two of the angles of a triangle, you can always work out what the remaining angle is by seeing what you need to add on to get to 180°.
There are three special types of triangle that are often used in problems:
(a) Equilateral Triangles
An equilateral triangle has 3 equal sides and 3 equal internal angles. As the internal angles of a triangle always add up to 180°, sharing these equally means that each internal angle is 60°.
(b) Right Angled Triangle
A right angle is usually shown as a square where two edges meet - this is always going to be 90°. The other two angles of the triangle must also add up to 90° so if you know one, you can easily work out the other.
(c) Isosceles Triangle
An isosceles triangle has two identical angles. This video explains how you can use this information.
5. The internal angles of a quadrilateral always add up to 360°
This video from White Rose proves why this is always true.
Put together everything you know
This video explores a previous SATs question in which a number of the facts we have looked at above needed to be used in order to calculate a missing angle.
