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Maths help: How do you measure angles? How do you use a protractor? How do you draw angles when you know the degrees?

Updated on October 13, 2013

What is an angle?

An angle is a combination of two lines (called arms), which both have the same start point (called vertex). The angle measures the amount of turn between the two lines and is measured in degrees.

The angle measures the amount of turn between the two arms and is usually measured in degrees or radians.

Angles are given different names depending on the amount of turn the angle has. These names and angles definitions are something you should get familiar with as this is a great check to your work on measuring angles.

The different types of angles

Type of angle
Description
Acute
An angle less than 90 degrees
Right angles
An angle that is 90 degrees
Obtuse
An angle which is greater than 90 degrees but smaller than 180 degrees
Straight
An angle of 180 degrees. (A straight line)
Reflex
An angle greater than 180 degrees
Full rotation
This is a full 360 degrees

And here they are for you to see:

The different types of angles
The different types of angles | Source

Do you find angles hard to figure out?

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How do we measure angles?

There is a very useful tool to measure angles and that is called a protractor.

A picture of one is seen below.

Most schools have and use a protractor like the one below so I will use this for my examples. There are protractors which are complete circles though but they can be used in the same way.

A protractor

A protractor
A protractor | Source

How do you use a protractor to measure an angle?

There are a number of steps you need to follow when using a protractor:

  1. First thing you need to do is place the centre of the protractor (usually has perpendicular lines meeting and a circle highlighting this) on the start point of the two lines.
  2. Next you need to make sure that the line on the bottom of the protractor fits over one of the lines of the angle. (Make sure the other line is behind the protractor and you won't go wrong with this step.)
  3. Then you need to follow the line at the bottom of the protractor to the zero on the scale. This will either be the bottom scale or top depending on which way the angle goes.
  4. Where the line meets the zero, this is the scale you use and then you count round until the second line intersects the scale. This number is the angle in degrees.
  5. Check your reading with the maths you already know about angles - i.e. if you have an angle drawn less than 90 degrees (acute angle) but you read the scale at say 130 degrees then you are reading the wrong scale on the protractor.

Example 1

What did I do to work out the angle of this example?

So in the above example, the first two steps have already been done:

  1. I placed the middle of the protractor at the starting point of both lines
  2. I then placed the protractor over one of these line making sure the other line is behind the protractor so I can read the angle.
  3. Next I needed to work out which scale to read off - the top scale or the bottom scale on the protractor. I know the scale I am after must have the zero where the line runs over it. So I look down the line and see that it is the bottom scale I need. (If I look at the top scale then it would start at 180 degrees so this isn't what I need.)
  4. i can then read off the angle where the second line meets the scale. So if I run my eyes along the scale I get to 80 degrees. It doesn't intersect at this point but one of the dashes after this point. I know that each 'dash' is equal to one degree as there are 10 'dashes' so I know the angle I am after here is 81 degrees.
  5. Now I can perform a basic check. I can see straight away that this angle is an acute angle so I know its less than 90 degrees. My answer is less than 90 degrees so I am happy.


Example 2:

How did I work out the angle for example 2?

Again, the first two steps are done for you in the example above:

  1. I placed the middle of the protractor at the starting point of both lines.
  2. I then placed the protractor over one of these line making sure the other line is behind the protractor so I can read the angle.
  3. Next I needed to work out which scale to read off - I followed the line to the left until I found the zero on one of the scales. This was the top scale this time as the first scale I came to (the bottom one) was 180 where the line met it.
  4. I can then read off the angle where the second line meets the scale. I run my eyes along the scale to where the line intersects it. I get to 20 degrees, but know I need to continue and count the number of 'dashes' to find out the angle. I count four dashes after my line so the angle is 24 degrees.
  5. Now I can perform a basic check. Straight away I know this is an acute angle so I know its less than 90 degrees. My answer is less than 90 degrees so I am happy again.

How do you use a protractor to draw an angle?

There are certain steps you need to follow when drawing an angle:

  1. First draw one of the lines. (This does not have to be a long line; around 4-5 cm, an inch, is fine)
  2. Next place the middle of the protractor on the end of the line. It does not matter which end you choose here.
  3. Run your eye down the line to where the line intersects the scale. Where it runs past the zero on the scale this is the one you use.
  4. Next work your way up the scale to where the angle you require. Next mark this angle off.
  5. Take the protractor away and draw a line from where the mark of the angle is to the starting point of the angle.

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