What does a child have to do to solve an angle relation in the 11+?

Calculate one unknown angle using a stated line, point, triangle, or quadrilateral relation. It is one of 55 named maths skills in the 11+, in the geometry strand, and this page carries 1 interactive exercise that practises it.

What is the trap in an 11+ solve an angle relation question?

A long pair of sides does not make a bigger angle, and the drawing is not there to be measured - the sum is what settles it. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What is not part of solve an angle relation in the 11+?

The skill map draws the line here: One relation or one short chain. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside solve an angle relation?

The geometry strand holds 15 skills that are tested together, and the pages next to solve an angle relation are track cube faces from a net, translate a coordinate and classify an angle. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise solve an angle relation for free?

Use Angle Chaser, embedded on this page. It is the exercise the skill map attaches to solve an angle relation, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

Maths · Geometry

Solve an angle relation

Calculate one unknown angle using a stated line, point, triangle, or quadrilateral relation.

Watch the worked example

Open the video page

Unlock the Missing Angle

This video shows how to use angle rules for lines, points, triangles or quadrilaterals to calculate a missing angle. Watch an 11+ maths question solved step by step.

0:00 / 2:41

Turn on captions with the CC button. Jump to any part with the chapter buttons.

Read the transcript

Keep practising with Trace Learn. Find topics to practise next

Quick quiz: Solve an angle relation

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz

Question 1
Iris marks every angle on this quadrilateral. What is the size of angle C?
- A.68°
- B.113°
- C.112°
- D.58°
Question 2
Maya marks every angle on this quadrilateral. What is the size of angle A?
- A.127°
- B.96°
- C.43°
- D.137°
Question 3
Zara marks every angle on this quadrilateral. What is the size of angle D?
- A.140°
- B.51°
- C.119°
- D.61°
Question 4
Esme marks every angle on this pentagon. What is the size of angle C?
- A.139°
- B.108°
- C.72°
- D.62°
Question 5
Esme marks every angle on this pentagon. What is the size of angle A?
- A.134°
- B.140°
- C.124°
- D.46°
Question 6
Esme marks every angle on this pentagon. What is the size of angle C?
- A.101°
- B.69°
- C.123°
- D.111°
Question 7
Theo marks every angle on this pentagon. What is the size of angle D?
- A.99°
- B.116°
- C.109°
- D.71°
Question 8
Bruno marks every angle on this quadrilateral. What is the size of angle A?
- A.100°
- B.99°
- C.110°
- D.70°
Question 9
Callum marks every angle on this pentagon. What is the size of angle E?
- A.62°
- B.118°
- C.115°
- D.108°
Question 10
Otis marks every angle on this quadrilateral. What is the size of angle C?
- A.77°
- B.93°
- C.87°
- D.97°

Practise it now

Watch each rule prove itself, then chase the missing angle one rule at a time.

It covers most of this skill rather than all of it.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Angles that add up to a fixed total

Rosa marks every angle on this triangle. What is the size of angle B?

Every angle of this triangle is marked except one, and the angles inside a triangle always add up to 180°.

73°
45°
135°
35°

Answer: 45°

How you get there

The marked angles are 73°, 62°, which comes to 135°, and the angles inside a triangle always add up to 180°, so angle B is 180° - 135° = 45°.

Why the other answers tempt

A long pair of sides does not make a bigger angle, and the drawing is not there to be measured - the sum is what settles it.

If they are stuck, say this

Add up the angles that are already marked, then take that total away from 180° - the angles inside a triangle always add up to 180°.

Now do it live in Angle Chaser

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's try Solve an angle relation together. Take a look at the picture. Here is what matters: Every angle of this triangle is marked except one, and the angles inside a triangle always add up to 180°. Here comes the question: Rosa marks every angle on this triangle. What is the size of angle B? A handy clue is: Add up the angles that are already marked, then take that total away from 180° - the angles inside a triangle always add up to 180°. Nice work. Here is the thinking: The marked angles are 73°, 62°, which comes to 135°, and the angles inside a triangle always add up to 180°, so angle B is 180° - 135° = 45°. So our answer is: 45°. One sneaky trap is: A long pair of sides does not make a bigger angle, and the drawing is not there to be measured - the sum is what settles it. Can you show me the first move in your own words? No rush; one calm step is enough.

What this exercise is doing

Angle Chaser

Watch each rule prove itself, then chase the missing angle one rule at a time.

An angle chase is a chain of rules, never a sum you can guess. The reflex is to take the number you can see away from 180 and hope, and in this picture that reflex is wrong: it is on the list of choices every time so you can watch it fail. What actually works is to look at HOW the lines meet.

Step 1. Prove the rules. Drag each rule until it proves itself.
Step 2. Chase it. Pick the rule, then dial the number.

What to say if they get stuck

Do not reach for a number yet. Ask which RULE you are allowed to use, and only then work out what it gives you.
This one takes 2 rules stacked up. Find an angle you CAN work out first, even if it is not x.
Here the Z pair carries the angle across to the other parallel line, and only then does the straight line finish it off.

Open Angle Chaser on its own page to share it

Related maths skills

Classify an angleClassify one angle by size or compare it with a reference turn.
Compose coordinate transformationsApply two stated coordinate transformations in order.
Identify a cube netDetermine whether a net folds to a cube.
Identify a shape propertyIdentify one stated property of a 2D or 3D shape.
Identify line symmetryIdentify or complete a reflection across one mirror line.
Identify a geometric transformationIdentify the translation, rotation, or reflection relating a shape and its image.
Plot or read a coordinateRead or place one point on a coordinate grid.
Preserve measure under a rigid transformationUse the fact that translation, rotation, and reflection preserve lengths and angles.
Reflect a coordinateDetermine a point image after reflection in a stated coordinate axis.
Reflect a shapeIdentify the result of one reflection in a stated mirror line.
Rotate a coordinateDetermine a point image after a stated rotation about the origin.
Rotate a shapeIdentify the result of one stated rotation.

All maths 11+ skills

Questions parents ask about solve an angle relation

What this skill involves, common mistakes and ways to practise it at home.

: Calculate one unknown angle using a stated line, point, triangle, or quadrilateral relation. It is one of 55 named maths skills in the 11+, in the geometry strand, and this page carries 1 interactive exercise that practises it.
: A long pair of sides does not make a bigger angle, and the drawing is not there to be measured - the sum is what settles it. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Add up the angles that are already marked, then take that total away from 180° - the angles inside a triangle always add up to 180°.
: The skill map draws the line here: One relation or one short chain. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The geometry strand holds 15 skills that are tested together, and the pages next to solve an angle relation are track cube faces from a net, translate a coordinate and classify an angle. Each has its own exercise and its own link, and none of them needs an account.
: Use Angle Chaser, embedded on this page. It is the exercise the skill map attaches to solve an angle relation, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.