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

Parallelmeans that two lines are always the same distance away from each other, and therefore will never meet never meet. Parallel lines are marked with matching arrows.

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

### Alternate Angles:

Alternate angles  are the same.

$D = C$

They are found in aZ-shape, and sometimes called “Zangles

### Corresponding Angles

Corresponding angles are the same.

$F = E$

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

### Vertically aligned angles

Vertically aligned angles are the same

$A + B$

These are angles around a point, always opposite from one another.

### Interior / Aligned angles

Allied angles add up to $180\degree$

$H + G = 180\degree$

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

These form a C-Shape.

### Example:

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

$BD$ and $EG$ are parallel lines.

State which angle fact you used at each step.

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

This means we will need multiple steps. (there are a few ways to do this)

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

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. How else might you do it?

### Example Questions

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

$\text{angle EFC } = 48\degree$

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

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

There are other possible methods for doing this question. As long as you’ve correctly applied angle facts, explained each step, and got the answer to be $48\degree$, your answer is correct.

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

$\text{angle CDG } = 121\degree$.

Secondly, because angles on a straight line add to 180, and angles CDG and CDA are on a straight line, we get

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

Thirdly, again using the fact that angles on a straight line add to 180, 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, 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 1-3

Level 4-5

Level 1-3

Level 4-5

Level 4-5

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