# Angles and parallel lines · Year 8

> Angles and parallel lines, Year 8: Angles as expressions in x and more. Explanation, worked examples and free practice for the national curriculum in England.

In Angles and parallel lines (Year 8) you practise 3 skills: Corresponding and alternate angles · Finding an angle between parallel lines · Angles as expressions in x.

When a line crosses two parallel lines, it makes two crossings, with four angles at each one: eight angles in all.

Corresponding angles are in the same position at the two crossings: for example, both above the line and to the right of the transversal. Between parallel lines, corresponding angles are equal.

Alternate angles are between the two lines, on opposite sides of the transversal. They are equal too when the lines are parallel.

You already know that vertically opposite angles are equal, and that angles on a straight line add up to 180°. With these rules you can find all eight angles from just one.

**Tip:** Corresponding and alternate angles are equal only when the lines are parallel. Check first whether they are parallel.

## What you learn

### Corresponding and alternate angles

- Example: The picture shows two parallel lines and a line crossing them. (Two parallel lines, and a third line crossing both. The angles it makes are numbered 1 to 8.) Choose a pair of corresponding angles.
- Options: 1 and 3 · 1 and 5 · 3 and 4 · 4 and 6
- Answer: 1 and 5
- Solution: Angles 1 and 5 are in the same position at the two crossings, so they are corresponding angles.

### Finding an angle between parallel lines

- Example: The picture shows two parallel lines and a line crossing them. (Two parallel lines, and a third line crossing both. The angles it makes are numbered 1 to 8.) Angle 5 is 35°. What size is angle 1?
- Answer: 35 °
- Solution: Angles 5 and 1 are corresponding angles, so they are equal: angle 1 is 35°.

### Angles as expressions in x

- Example: The picture shows two parallel lines and a line crossing them. (Two parallel lines, and a third line crossing both. The angles it makes are numbered 1 to 8.) Angle 1 is x + 21 , and angle 5 is 3x − 95 . What is the value of x ?
- Answer: 58
- Solution: Angles 1 and 5 are corresponding angles, so they are equal: x + 21 = 3x − 95 Rearrange: 2x = 116 Divide both sides by 2: x = 58

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

[Practise on the site](https://kixplo.com/uk/en/) · [All Year 8 topics](https://kixplo.com/uk/en/maths/year-8/)