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Introducing the Angle (Years 5 – 7) This wheel has four parts. So the angle of each part is 360 (the total angle) divided by 4. Can anyone tell me what 36/4 is? The angle between the lines of each segment is 90º. This is the same as the corner of a square, or a piece of paper. This special angle is called a right angle, and is shown by drawing a little square in the corner where the two lines meet (right). Each corner of a square or a rectangle is 90º, there are 4 corners so the total of all the angles in a square is 360º. The way in which we measure how far apart two lines that are joined at one end are without referring to distance is to find the angle between them. Angles are defined by splitting a circle into 360 parts or segments, where all of the lines cross through the centre. Each part is called a degree, so one part out of all of the 360 parts is 1 degree, and the angle of the whole circle is 360º.
If we were to remove one of the spokes on this wheel, we can see a straight line across the centre of the wheel. The angle of a straight line is 90º + 90º = 180º. We draw a small semi-circle over the 2 spokes to represent the angle. The next wheel is a shipping wheel with 6 spokes or parts. The angle of each part is 360/6 = 60º. An equilateral triangle is a triangle whose sides are all the same length. The angle of each corner of this type of triangle is 60º. The sum of all of the angles in any triangle is 60º + 60º + 60º = 180º.
The next picture shows a similar shipping wheel but this wheel is split into 8 parts. This is like the first wheel (the bike wheel) we looked at that was split into 4 parts, except that in this case each of those 4 parts is split into 2 so that we get a total of 8 parts. A quarter of a circle has an angle of 90º, half of this is 45º. So each part in this wheel has an angle of 45º. This bike wheel has 3 spokes, so the angle of each part is 360/3 = 120º. Angles between 0 and 90º are called acute angles. Angles between 90º and 180º such as the angles in this wheel are called obtuse . Angles that are greater than 180º (a straight line) are called reflex angles.
This is a car alloy that has 5 spokes. The angle of each part is 360/5 = 72º. This angle is less than 90º so it is an acute angle. The angle between the first spoke at the top and the fourth spoke (moving clockwise) is 72º + 72º + 72º = 216º (right image) . This angle is greater than 180º and so it is a reflex angle.
To measure the angle of each part of the bike wheel or between any two lines joined at one end you use a protractor, which is like a ruler for angles. The protractor is a semi-circle with the degrees marked on the round edge. By placing the straight edge of the protractor along one of the lines you can determine the angle by following the second line (16 spokes, angle = 22.5º).