Angle Basics

Angle Basics

KS3AQAEdexcelOCRWJEC

Angle Basics

Understanding the basics of angles will help you with many other geometry topics. We will cover the different types of angles, angle notation and how to measure angles in this topic.

Skill 1: Types of Angles

There are four types of angles you need to know. These are:

  • Right-angles – these are equal to 90\degree and are indicated by a square corner.
  • Acute angles – these are small angles less than 90\degree
  • Obtuse angles – these are angles larger than 90\degree but less than 180\degree
  • Reflex angles – these are the biggest angles and are larger than 180\degree

types of angles

Level 1-3 KS3 AQA Edexcel OCR WJEC

Skill 2: Angle Notation

There are a few different ways to label angles, but the most straightforward is to use three letters, where the middle letter indicates the position of the angle. The other two letters indicate the two lines that form the angle.

angle notation three letters
angle notation three letters

For example, in the image shown the angle \textcolor{#0070C0}{ADC} is the angle at the corner \textcolor{#0070C0}D formed by the lines \textcolor{#0070C0}{AD} and \textcolor{#0070C0}{DC}.

 

We could also write this angle as \textcolor{#0070C0}{\angle ADC} or \textcolor{#0070C0}{A\hat{D}C}

All three types of notation are perfectly acceptable.

We could also call this angle \textcolor{#0070C0}{CDA}. As long as the middle letter is where the angle is and the two other letters indicate the joining lines, they can appear in either order.

Level 1-3KS3AQAEdexcelOCRWJEC

Skill 3: Measuring Angles

Measuring angles requires the use of a protractor. Here are some helpful tips for using a protractor:

  • Line the middle of the protractor up with the angle ‘corner’
  • You need to make sure you are measuring from 0\degree, so be careful to line things up properly
  • Read the scale from 0 to the exact position on the line to measure the size of the angle
measuring angles with a protractor
measuring angles with a protractor

Example: Measure the size of the angle marked \textcolor{#0070C0}x

 

Following the steps above, the first thing is to line properly align the protractor. As can be seen, the cross in the centre of the protractor is situated directly over the point or ‘corner’ of the angle x.

The protractor is also aligned such that the ‘flat’ line of the angle is at 0\degree

Reading from 0, we can see that the other line crosses the scale at 145, so the angle \textcolor{#0070C0}{x=145\degree}

 

Be careful when using a protractor with two scales, like the one shown – ensure you are always reading from the correct position.

Level 1-3KS3AQAEdexcelOCRWJEC

Skill 4: Drawing Angles

Drawing angles requires also requires the use of a protractor. The same tips apply as for measuring angles using a protractor, however the process is slightly different.

drawing angles protractor use
drawing angles protractor use

Example: Mark another point labelled C such that the angle

ABC = 40\degree

 

The process is similar to measuring an angle but with a couple of differences.

 

Step 1 is to measure the angle and mark the location of the point. Again, place the centre of the protractor over the point B and align the scale so that the line AB goes through 0\degree. Mark the point \textcolor{red}C at 40\degree.

Step 2 is to draw the line between the points B and C

Level 1-3KS3AQAEdexcelOCRWJEC

Example Questions

Angle x is clearly larger than a right-angle (a square corner), but not as big as the angle in a straight line (180\degree). Therefore angle x is obtuse.

Angle y is also obtuse.

Angle z is larger than the angle in a straight line, so it is a reflex angle.

Angles BAD and BCD are both equal to 75\degree

 

Angles ABC and ADC are both equal to 105\degree

The angle PQR is equal to 60\degree

 

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