Corresponding Angles and Alternate Angles Worksheets and revision | Maths Made Easy

Corresponding Angles and Alternate Angles Worksheets and revision

Level 4-5

Corresponding and Alternate Angles: 4 Simple Rules

Corresponding and alternate angles are formed when a straight line passes through two parallel lines. 

Parallel means that two lines are always the same distance away from each other,  and therefore will never meet. Parallel lines are marked with matching arrows as shown in the examples below.

Drawing a straight line that passes through two parallel lines creates a whole bunch of angles that are all related to each other. How these angles are related is explained by 4 simple rules.

Level 4-5
Level 4-5

Alternate Angles:

alternate z angles

Alternate angles are the same.

\textcolor{red}{D} = \textcolor{skyblue}{C}

They are found in a Z-shape, and sometimes called “Z angles

alternate z angles
Level 4-5

Corresponding Angles

corresponding f angles

Corresponding angles are the same.

\textcolor{orange}{F} = \textcolor{blue}{E}

They are found in an F-shape and are sometimes called “F angles

corresponding f angles
Level 4-5

Vertically aligned angles

vertically opposite angles equal

Vertically aligned angles are the same

\textcolor{limegreen}{A} = \textcolor{purple}{B}

These are often called “vertically opposite angles“.

vertically opposite angles equal
Level 4-5

Interior / Allied angles

allied interior angles equal

Allied angles add up to 180\degree

\textcolor{maroon}{H} + \textcolor{green}{G} = 180\degree

These can be refereed to as either Allied angles or Interior angles.

allied interior angles equal
Level 4-5

Example: Angles in Parallel Lines

Find the angle marked x in the picture below.

BD and EG are parallel lines.

State which angle rule you used at each step.

[2 marks]

unknown alternate vertically opposite angle

Currently we cannot see a rule connecting \angle EFC with x

This means we will need multiple steps.

Firstly, we will use the fact that angles on a straight line add to 180 degrees.

Specifically, \angle EFC and \angle CFG add to make 180\degree.

Which means we can do the following:

\angle CFG  = 180\degree - 32\degree = 148\degree.

Now, looking at the diagram we can see that angle \angle CFG and the missing angle x are corresponding angles.

Therefore, we get

x = 148\degree.

alternate unknown vertically opposite angle

As mentioned, there are multiple ways to do this question.

Level 4-5

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Example Questions

Using corresponding angles, we find that \angle \text{AHB}  = \angle \text{FGH}, so \angle x = 37\degree

 

unknown corresponding f angle answer

First identifying that \angle \text{FGH}  and    \angle \text{GHC} are alternate angles, we get

 

\angle \text{GHC}=41\degree

 

Then as \text{BE} is a straight line we can use the fact that angles on a straight line sum to 180\degree,

 

x=180\degree-41\degree=139\degree

Firstly, because angle HFG and angle EFC are vertically opposite, we get

 

\angle \text{EFC} = 48\degree

 

Secondly, because angle EFC and angle BCA (\angle x) are corresponding angles, we get

 

\angle \text{BCA} = x = 48\degree

unknown vertically opposite corresponding f angle question answer

Firstly, using the fact that angles FGJ and CDG are corresponding angles, we get

 

\angle \text{CDG } = 121\degree

 

Secondly, because angles on a straight line add to 180\degree, and angles CDG and CDA are on a straight line,

 

\angle \text{CDA } = 180 - 121 = 59\degree

 

Thirdly, again using the fact that angles on a straight line add to 180\degree, and angles CDA, BDE, and ADB (otherwise known as angle x) are on a straight line, we get

 

x + 50 + 59 = 180,\text{ so } x = 180 - 109 = 71\degree

 

unknown angle around a point answer

Firstly, because angles BEF and EHJ are corresponding angles, we get

\text{angle EHJ } = 39\degree.

 

Next, because angles EDH and DHG are alternate angles, we get

 

\text{angle DHG } = 76\degree.

 

Then, because angles DHG, DHE, and EHJ are angles on a straight line and angles on a straight line add to 180\degree, we get

 

\text{angle DHE } = 180 - 76 - 39 = 65\degree

 

Finally, because angle DHE and angle x are vertically opposite angles, we get

 

x = 65\degree.

 

unknown angle in a triangle question answer

 

There are other possible methods for doing this question. As long as you’ve correctly applied angle fact, explained each step, and got the answer to be 71\degree, your answer is correct.

Worksheets and Exam Questions

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