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Angle Chase

Use knowledge and reasoning to fill in the angles on the geometrical diagrams drawn inside rectangles.

Chase 1 Chase 2 Chase 3 Chase 4 Exam-Style Description Help More Angles

This is Angle Chase level 2. You can also try:
Theorems Triangles Points Parallels Chase 1 Chase 3 Chase 4


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if should go offline for whatever reason, there is a mirror site at that contains most of the resources that are available here on

When planning to use technology in your lesson always have a plan B!

Heather Scott, Twitter

Sunday, October 8, 2017

John Tranter, Transum

Friday, October 13, 2017

"I wrote this activity for a friend's daughter who was struggling to see the angle relationships in her school homework. I presented it to her as this self-checking digital version because if she tried the more traditional paper versions she would not get the immediate feedback the computer provides.

We did level one together. She typed in the answers in the web browser but had a laminated copy of the printed version in front of her to draw on (Great for seeing the Z shapes).

After Level 1, she was feeling more confident so we played Level 2 as a game, taking it in turns to figure out one of the angles. She was most confident with vertically opposite angles and angles in triangles. A blank sheet of paper to hide the unnecessary part of the diagram helped her spot the angles together on a straight line. At one point, using her own initiative, I found her looking in her school exercise book to remind herself about angles in quadrilaterals and pentagons.

This was one of those great teacher moments when you can see the understanding taking shape and the pride the student demonstrates when solving mathematical problems.

I hope this activity works as well for you. "


Tuesday, February 6, 2018

"Why are the corner angles 90? I can't see it.

[Transum: Very good question Shirley. You can't assume angles are exactly 90° just because they look like right angles. The clue here is in the text at the top of the page which says that the diagram is drawn inside a rectangle and the angles of a rectangle are 90°.]"

Priscilla Allan,

Thursday, November 15, 2018

"Loved this so much - We want MORE! Thanks - it is awesome fun."

Rebecca Rouse, Sydney, Australia

Monday, November 30, 2020

"Hi John,
We're so stuck on #4. Any hints?
Cheers, Rebecca.

[Transum: Glad to hear that you are having fun with Angle Chase. There is a circle involved so your clue is to have a look at Circle Theorems. Good luck, John]"

QEH, Bristol

Friday, January 22, 2021

"Year 7 have been solving geometry problems this week.
Zac took about 2 hours to complete this one because he had to learn about circle theorems and parallel lines.
Independent study leads to some amazing learning."

Andrea Biro, Twitter

Friday, March 11, 2022



Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


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Description of Levels



Level 1 - 31 angles to be found in a diagram with one set of parallel lines

Level 2 - 42 angles to be found in a diagram with three sets of parallel lines

Level 3 - 69 angles to be found in a fiendishly complex diagram

Level 4 - Impossible unless you know the circle angle theorems

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

More on this topic including lesson Starters, visual aids and investigations.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Angle Theorems

Theorem 1 Theorem 2 Theorem 3
Theorem 4 Theorem 5 Theorem 6
Theorem 7 Theorem 8 Theorem 9

Click on a picture above for a large version, theorem description and interactive model.

If you are on level 4 you will also need the Circle Theorems.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up