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

# Corresponding Angles and Alternate Angles Worksheets and revision

Level 4 Level 5

## What you need to know

### Parallel lines: 4 Simple Rules

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 below in the examples.

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

### Alternate Angles: Alternate angles are the same.

$D = C$

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

### Corresponding Angles Corresponding angles are the same.

$F = E$

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

### Vertically aligned angles Vertically aligned angles are the same

$A + B$

These are often called “vertically opposite angles“.

### Interior / Allied angles Allied angles add up to $180\degree$

$H + G = 180\degree$

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

### Example: Angles in Parallel Lines

Find the angle marked $x$ in the picture below.

$BD$ and $EG$ are parallel lines.

State which angle fact you used at each step.

[2 marks] 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 $\angle EFC$ and angle $\angle GFC$ 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

$x = 148\degree$. As mentioned, there are multiple ways to do this question.

### Example Questions

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

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

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

$x = 65\degree$. 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

Level 3-5

Level 3-5

Level 4-5

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