1.2 Angles

An angle is formed where two straight lines (or sides) meet. Angles are measured in degrees, which is shown by using the symbol ° after the number of degrees. So for example, 45° means an angle of 45 degrees.

There are 360° in a circle. There are 180° in a half-turn – that is, from north to south on a compass, or from 9 to 3 on a clock.

An angle of 90° is a quarter-turn – from north to east on a compass, or from 12 to 3 on a clock. These angles are also known as right angles. Right angles are shown like this:

Figure 3 A right angle

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An illustration of a right angle – that is, an angle of 90°.

Figure 3 A right angle

Right angles are very common in everyday life. Look around you and see how many you can spot.

Here are a few examples of where you might have noticed a right angle:

• the corners of your screen (a corner is where two lines meet)
• corners of windows
• the corners of a book page
• where the walls meet the floor
• where the table legs meet the top.

Angles of less than 90° are called acute angles. Angles of more than 90° are called obtuse angles.

Activity 2: Angles

Which angles in Figure 4 are right angles, acute angles or obtuse angles?

Figure 4 Angles

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Six illustrations of angles, labelled (a) to (f). Angles (a) and (f) are greater than 90°; angles (b) and (d) are less than 90°; angles (c) and (e) are exactly 90°.

Figure 4 Angles

Answer

Angles (a) and (f) are obtuse angles (greater than 90°).

Angles (b) and (d) are acute angles (less than 90°).

Angles (c) and (e) are right angles (exactly 90°).