Angles

Bearings are simply a way of giving directions (a bit more accurately than just relying on North, South, East and West!).

If they are given with a distance as well then you have an exact position.

Note:

1. Bearings are always measured from North, which is 000⁰ (or 360⁰). Always draw a North line at each point to give a guide for your protractor.

2. They are always measured clockwise and must have three figures. So East is 090⁰, South is 180⁰ and West is 270⁰.

If you are given the bearing and position of something from a point and asked to mark it in (after which you may be asked to measure something else) then here's what you do:

1. Draw a North line at the point you are measuring from.

2. Put your protractor on this point and line up 0⁰ with the North line. Always lean right over the paper when you're doing this even though you might think you look a bit stupid!

3. Read round the protractor clockwise until you reach the angle you want and mark it with a pencil.

4. Draw a pencil line from the point you are measuring from right through your angle point.

5. Check your scale (if there is one) and measure the distance you need along this line. Put a cross to show your position.

Don't rub any of your pencil lines out. These help to show what you've done.

Here's the kind of diagram you might have for a ship which is 8 km away from a lighthouse on a bearing of 125⁰ using a scale of 1 cm = 1 km.

To measure the bearing of something, call it B, from something else, call it A, here's what you do:

1. Draw a North line at A (because that's where you're measuring from).

2. Draw a pencil line connecting A to B. This acts as a guide for your protractor!

3. Place your protractor on A and line up 0⁰ with the North line.

4. Read round clockwise until you reach the line going to B. There's your Bearing! Don't forget to write it with three figures (if the angle is only two digits put a zero in front!).

An angle is formed where two straight lines meet. We measure them in degrees and there are 360 degrees in a full circle.

We can use the following facts to work out angles we don't know:

1. Angles around a single point add up to 360⁰.

2. Angles on a straight line add up to 180⁰. So the missing angle below must be 40⁰.

3. Vertically opposite angles are equal. (This is when two straightlines cross!).

4. Angles in a triangle add up to 180⁰. (See 'Polygons').

5. Angles in a quadrilateral add up to 360⁰. (See 'Polygons').

When a straight line crosses two parallel lines there are more angle factswe can look for and use!

1. Corresponding angles are equal - these are angles in a letter 'F'.

2. Alternate angles are equal - these are angles in a letter 'Z'.

3. Supplementary angles add up to 180⁰ - these are angles in a letter 'U' or 'C' (when the 'U' and the 'C' are made of three straight sides, of course).

The diagram below might help you to see this more clearly. Click on thepairs of angles you want to see and they will be shown on the diagram:

When you've learnt all the above facts, the difficult thing is spotting them in the first place! You need to try out your knowledge by practising questions and ignoring any lines that are 'in the way'! Geometry problems will now be a doddle!