# Recognise Alternate Angles

In this worksheet, students will learn how to recognise alternate angles.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions, Angles

Difficulty level:

### QUESTION 1 of 10

No, No, No all these different angle types to remember. All I ever want is to be an astronaut when I grow up!!!!

Unfortunately even astronauts might need to learn about different angles.

There is bad news and good news.

Bad News - There are various types of angles that you will need to recognise in diagrams

Good news - Once you have found them, for many there is no working out involved.

Here we are looking at alternate angles.

Alternate angles are the same size.

Fantastic - all we need to do now is recognise them.

1. They are found within a set of parallel lines. The parallel lines are usually marked with little arrows or dashes.

2. They are either side of the transversal (or the line cutting through the parallel lines to me and you)

3. They are sometimes called Z angles because they make a Z shaped. It is best use the proper name though.

4. As you can see they are equal in size.

That is all there is to it, you just have to be able to spot them in diagrams.

Which diagrams show alternate angles?

a

b

c

d

e

f

Which angle is alternate to g?

Which sets of angles are alternate to each other?

h and b

g and d

h and c

g and a

 a b c d 108° 72° The alternate angle to 72° is the angle measures

 a b c d 108° 72° The alternate angle to 72° is the angle measures

 a b c d 108° 72° The alternate angle to 72° is the angle measures

 69° 111° a° is alternate to b° is alternate to

 107° 73° The value of M is The value of J is

What is the value of x?

What is the measurement of angle e?

Write your answer in figures without the units.

• Question 1

Which diagrams show alternate angles?

a
e
EDDIE SAYS
Did you spot them quite quickly? a and e. Because the angles are both within the parallel lines on opposite sides of the transversal.
• Question 2

Which angle is alternate to g?

d
EDDIE SAYS
g is your starting point. You know an alternate angle is on the opposite side of the transversal AND within the parallel lines. So the alternate angle could only be d.
• Question 3

Which sets of angles are alternate to each other?

g and d
h and c
EDDIE SAYS
Sometimes these angles can be tricky to spot if there are several angles written down. g and d and h and c are INSIDE the parallel lines and on OPPOSITE sides of the transversal.
• Question 4

 a b c d 108° 72° The alternate angle to 72° is the angle measures
EDDIE SAYS
Hopefully you are able to spot these now quite easily. This is actually often the hard part. Alternate angles are always equal so angel c is 72°
• Question 5

EDDIE SAYS
Uh oh... this looks a bit different. Oh teachers do like to mix things up a bit, just as you were getting comfortable. Look for the parallel lines and the transversal, that is all you need. x is alternate to the 48° and we know that alternate angles are equal. Its great when there is no working out involved isn't it.
• Question 6

EDDIE SAYS
Start at the 65° jump across the line, stay inside the parallel lines and hey presto there you are. a is alternate and is also 65° Quite often you are asked to explain your answer so you just say 'alternate angles are equal'.
• Question 7

 69° 111° a° is alternate to b° is alternate to
EDDIE SAYS
I always think of alternate as being on the other side. Alternate can mean different so that is how you can remember they are on different sides of the transversal. That is where the difference ends because the angles are the same.
• Question 8

 107° 73° The value of M is The value of J is
EDDIE SAYS
How is the confidence in spotting these coming along? M is alternate to 107°, and J is alternate to 73° It is when they are shown in a slightly different way things can become difficult. and so for my next trick..
• Question 9

What is the value of x?

76
EDDIE SAYS
Okay, I did warn you that this may not be as easy to spot. Also as an added bonus, you need to recall some facts about an isosceles triangle. If you extend the line at the top of the triangle you can clearly see a set of parallel lines. You need to find one of the base angles of the isosceles triangle. 180 -28 = 152. Base angles in an isosceles triangle are the same so 152 ÷ 2 = 76°. Put this into your triangle and you can see that 76 is alternate to x.
• Question 10

What is the measurement of angle e?

Write your answer in figures without the units.

70
EDDIE SAYS
We had to finish with a flourish, of course we did. This isn't as bad as it looks. We can see there are parallel lines. We can see that b is alternate to e. We can also see that the triangle is isosceles because of the markings on the side. We know that the base angles are the same so that we can now find angle b. 180 - 40 = 140° 140 ÷ 2 = 70°. Alternate angles are equal so e is also 70° Now may be astronaut training could be back on the cards..
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started

Start your £1 trial today.
Subscribe from £10/month.

• Tuition Partner