# Angles

## Bearings

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.

#### Finding a position

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.

#### Measuring bearings

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!).

## Exam-style Questions

1. a) What fraction of a complete turn is:

(i) North to East,

(1 mark)

(ii) North to South-East

(1 mark)

b) Jill faces West. She makes a ¼ turn anticlockwise. What direction does she face now?

(1 mark)

c) How many degrees are there in a ¼ turn?

(1 mark)

(Marks available: 4)

Answer outline and marking scheme for question: 1

a) (i) One quarter

(ii) Three eighths

b) South

c) 90°

(Marks available: 4)

2. In the diagram the lengths of AB, BE, EC and CD are equal.

Angle EBC = 64°.

a) Find the value of

(i) x,

(2 marks)

(ii) y,

(2 marks)

What special name is given to this quadrilateral?

(2 marks)

(Marks available: 6)

Answer outline and marking scheme for question: 2

a)(i) 52°

(ii) 32°

b) Rhombus

(Marks available: 6)

## Angles

#### Angle facts

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').

#### Parallel lines

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!

## S-Cool Revision Summary

 Types of Angles What they do... Round a point Add up to 360o On a straight line Add up to 180o Vertically Opposite Equal In a triangle Add up to 180o In a quadrilateral (4-sided polygon) Add up to 360o Alternate (Z-angles) Equal Corresponding (F-angles) Equal Supplementary (C or U angles) Add up to 180o

## Bearings Notes

1. Always use three figures.
2. Always draw North lines.
3. Always measure from North being 0o.
4. Always measure clockwise.
5. Always put in pencil lines connecting the points and don't rub them out at the end.
6. Always put your protractor on the place you're measuring from and not to.
7. Be as accurate as your can (sharp pencil, lean over diagram!).