JSS1 Mathematics Third Term: Identification and Properties of Angles

Angles as Rotation

We use the word angle for amount of turn. For example the figures below show the hands of a clock move between 12 ‘clock to 12 ‘ clock.  Both hands turn. In one hour the amount that each hand turns is different

The minute hand makes one complete turn, or one revolution

The angle turned = 1 revolution.

As we can measure length, we can measure angle. To avoid fractions, one revolution is divided into 360 equal parts. Each part is called a degree. We use the symbol ­ ⁰ for degree.

1 revolution = 360 degrees or 360⁰

1⁰ = 1/360 revolution

Angles between lines

The figure below shows two lines AB and CB. The lines meet at the point B.

The angle between the two lines is the amount that one line must turn so that it points the same way as the other line.

Example

What is the angle between the hour hand and the minute hand of a clock at 1 o’clock?

The angle between the hands is the amount that one hand must turn to reach the position of the other. That is 1/12 of a revolution.

angle between hands = 1/12 of a revolution

= 1/12 of 360⁰ = 30⁰

Notice, in the above example, that the size of the angle does not depend on the size of the hands. At 1 o’clock the angle between the hour hand and the minute hand is 30⁰ whether on a watch or on a clock.

Watch                      Clock

Again notice from the figures above that 330⁰ would also be a correct answer to the previous example above. The minute hand would turn through 330⁰ if it went the other way round.

330⁰ + 30⁰ = 360⁰

Copy and complete the table below

revs	degrees
1	360
2
3	1080
10
1/12	180
1/3
	90
1/10
1/8
1½

Naming angles

When lines BA and CB meet at the point B in the figure below, we say that angle ABC or angle CBA is the angle between them. Notice that B, the middle letter, is the vertex of the angle. The lines AB and OB are the arms of the angle.

If BA is fixed and CB can turn, we get angles of different sizes. Some of these have special names.

The right angle is especially important. There are many examples where lines meet at right angles. A right angle is often shown on a diagram by drawing a small square at the vertex of the angle.

Read more below-

ANGLES: Identification and Properties of Angles