1.2 How to measure an angle
To measure an angle you need a protractor. The protractor shown here is a semicircle that is graduated to measure angles from 0° to 180°. It is also possible to buy circular protractors that measure angles from 0° to 360°.
The diagram below indicates how the protractor should be positioned in order to measure an angle. Place the base line of the protractor on one arm of the angle, with the centre O on the vertex. The angle can then be read straight from the scale. Here 
= 40° (not 140°).
Be careful to use the correct scale. In this case the angle extends from the line OY up to the line OX, so use the scale that shows OY as 0° – the outer scale in this instance.
In the above example, one of the arms of the angle is horizontal. However, sometimes you may find that you need to position the protractor in an awkward position in order to measure an angle.
You can also use a protractor to construct an angle accurately, but once you have drawn the angle, be on the safe side and measure it to check that it is correct.