Angles
Comparing angles
An angle is a measurement of turn. In this unit you compare angles to say which is greater and put a group of angles in order of size.
An angle is a turn
An angle measures how far something turns. The bigger the turn, the bigger the angle. A quarter turn makes a right angle. At 3 o'clock, the hour and minute hands of a clock make a right angle.
Length does not change the angle
The length of the lines and the thickness of the lines do NOT change the size of an angle. Only the amount of turn matters. Two angles can be exactly the same size even if one is drawn with longer lines.
Comparing with tracing paper
To compare two angles, trace one angle onto tracing paper. Then place it over the other angle. Match one line and put the corners (points) of the angles together. Now you can see which angle is greater.
Putting angles in order
To order a group of angles, compare them two at a time. Then arrange them from the smallest turn to the largest turn. With practice, you can often tell which angle is greater just by looking.
Worked examples
Which angle is greater?
- Compare a 40° angle and a 70° angle.
- The bigger the turn, the bigger the angle.
- 70° is a bigger turn than 40°.
Answer: The 70° angle is greater.
Comparing by tracing
- Trace angle A onto tracing paper.
- Place it over angle B, matching one line and the corner.
- Angle A covers more turn than angle B.
Answer: Angle A is greater than angle B.
Ordering angles
- Compare 30°, 60° and 90°.
- Find the smallest turn first: 30°.
- Then 60°, then 90°.
Answer: In order: 30°, 60°, 90°.
Where you see this in real life
- Dancers making sure their feet are all at the same angle.
- The hands of a clock making different angles through the day.
- Cutting a cake into pieces and comparing the angles of the slices.
Key words
- Angle
- A measurement of turn between two lines that meet at a point.
- Compare
- To decide which of two things is greater or smaller.
- Right angle
- The angle of a quarter turn.
- Order
- To arrange things from smallest to largest (or the other way).