# EdPlace's Year 9 home learning maths lesson: Angles in Parallel Lines

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**Get them started on the lesson below **and then jump **into our teacher-created activities** to practice what they've learnt. We've recommended five to ensure they feel secure in their knowledge - 5-a-day helps keeps the learning loss at bay (or so we think!).

Are they keen to start practising straight away?** Head to the bottom of the page to find the activities. **

**Now...onto the lesson!**

**Key Stage 3 Statutory Requirements for Maths**

**Year 9**

*students should*

*Understand and use the relationship between parallel lines and alternate and corresponding angles.*

# What's It All About?

A common question in exams is finding the missing angles on a set of parallel lines. This guide will show how to demonstrate the rules to remember. Once you recall the rules of parallel lines, calculating any missing angle will become very straightforward.

1) **D**** escribe **a pair of angles as alternate, corresponding or co-interior,

2) **Recall** the relationships between these types of angles

3) **Calculate** missing angles in parallel lines, using the rules learned.

## Where to Start?

Begin by drawing a pair of **parallel lines**, then draw a diagonal line cutting through them.

## Step 1

Measure the two **angles** at the top of the shape. If you don’t have a protractor to hand, let’s say the **angles** are 120° and 60°.

You should know that **angles** on a straight line always add up to 180° and **angles** around a point add up to 360°.

## Step 2

Here is where the relationships between the **angles** become obvious. Let’s measure every **angle** on this shape:

As we can see, **all the acute angles are the same and all the obtuse angles are the same. **This is an important thing to remember. There are eight **angles** here but only two different values.

## Step 3

As long as we have a diagram of the **angles** on **parallel lines**, we can start highlighting parts of it to understand the rules to remember. You can remember them with letters:

**If we draw a “Z” on the lines, we can highlight a pair of acute angles (or a pair of obtuse angles).**

**These are called alternate angles. They are always ****equal****.**

**Now let’s draw an “F” over the lines and highlight the ****angles**** within the letter:**

**These are called corresponding angles and are always ****equal****.**

**Returning to the original diagram:**

The top four angles** correspond **to the bottom four.

**The idea of “corresponding” angles is that the top of the picture exactly matches the bottom. **Both the 120° angles on the left-hand side **correspond**; both the 60° angles on the right-hand side **correspond**; and so on.

**Finally, let’s draw a “C” over the lines and highlight the two angles within it:**

**The way to think of this is a straight line that has been “bent up”. This pair of angles are called co-interior angles and they will always add up to 180°.**

## Step 4 - Putting it into Practice

To summarise what we have learned in Step 3:

1. **Alternate** “Z” **angles** are always **equal**.

2. **Corresponding** “F” **angles** are always **equal**.

3. **Co-interior** “C” **angles** always add up to 180**°**.

The last thing to emphasise is that these rules **only work if the lines are parallel**. A common mistake that students make is applying these rules on lines that are **not parallel.**

For example:

It is clear to see that the top of the picture does not match the bottom. **Angles** on a **straight line** still add up to 180° and **angles** around a point still add up to 360° but there is no other connection between the two sets of.

Practice questions

Using the guide, see if you can now work out these missing angles and give reasons for your answers:

(a)

(b)

(c)

## Step 5 - Give it a go...

Why not test your child's understanding and see if they can tackle these activities?

All activities are **created by teachers and automatically marked.** Plus, with an EdPlace subscription, we can **automatically progress your child** at a level that's right for them. Sending you progress reports along the way so you can **track and measure progress, together** - brilliant!

Activity 1 - Angles on parallel lines

Activity 2 - Angles in Triangles and on Parallel Lines (1)

Activity 3 - Angles in Triangles and on Parallel Lines (2)

Activity 5 - Exterior angles of regular polygons

**Answers**

(a) a = 150°. Co-interior angles add up to 180°.

(b) b = 100°. Alternate angles are equal.

(c) c = 70°. Corresponding angles are equal.

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