Four facts cover nearly everything: angles on a line (180°), around a point (360°), in a triangle (180°), vertically opposite (equal). Learn those four properly, practise spotting them inside busy diagrams, and your child will unlock a large slice of the geometry marks in any modern 11+ paper. This page teaches the skill step by step, shows the traps that cost marks, and points you to the free graded worksheets and timed mocks that make it stick.
What 11+ angles questions actually test
At 11+ level, "angles" means recognising and combining angle facts rather than measuring with a protractor. Papers rarely ask a child to draw an angle; they show a diagram with one or two missing values and expect the child to reason to the answer. The core skills are: naming angle types (acute, right, obtuse, reflex, straight), applying the four key facts, and working through two-step problems where one found angle unlocks the next. Our free worksheet library grades every angles topic across four tiers — Foundation, Developing, Secure and Greater Depth — so a child can enter at their level and climb.
The angle facts to memorise
Nearly every 11+ angles question rests on the short list below. Have your child recite these until they are automatic, because the exam gives no formula sheet.
| Rule | Angle fact |
|---|---|
| Angles on a straight line | Add to 180° |
| Angles around a point | Add to 360° |
| Angles in a triangle | Add to 180° |
| Angles in a quadrilateral | Add to 360° |
| Vertically opposite angles | Are equal |
| Right angle / angles in a square corner | 90° |
An angle type reminder helps too: acute is under 90°, a right angle is exactly 90°, obtuse is between 90° and 180°, a straight angle is 180°, and reflex is over 180°. Children who confuse obtuse and reflex lose easy marks, so drill the vocabulary alongside the calculation.
A worked example, step by step
Here is a classic two-step question in the GL style. A triangle has angles of 55° and 65°, and the third angle sits on a straight line next to an unknown angle x. Find x.
- Find the third angle of the triangle: angles in a triangle add to 180°, so 180 − 55 − 65 = 60°.
- Use the straight line: that 60° and x sit on a straight line, so they add to 180°. Therefore x = 180 − 60 = 120°.
- Sense-check: 120° looks obtuse in the diagram, which matches — so the answer is reasonable.
The habit that wins marks is the sense-check. Teach your child to glance back at the diagram and ask "does an obtuse-looking angle really measure 120°?" A quick visual check catches most slips before they are committed to the answer sheet.
Common mistakes and exam traps
- Reading the wrong angle: in a busy diagram the child solves for a neighbouring angle instead of the marked one. Circle the target angle first.
- Assuming a diagram is to scale: 11+ diagrams are often "not drawn to scale". Never estimate by eye when a rule gives the exact value.
- Stopping one step early: two-step questions reward the second calculation. Finding 60° and forgetting to subtract from 180° is the single most common angles error.
- Arithmetic slips: 180 − 47 done in a hurry becomes 143 instead of 133. Encourage rounding-and-adjusting as a check.
- Mixing up 180° and 360°: a straight line is 180°, a full turn around a point is 360°. Confusing them wrecks otherwise sound reasoning.
How angles appear in a real GL 11+ paper
Most regions now sit GL Assessment papers after CEM's separate 11+ tests were phased out around 2022–2023. A GL maths paper is typically around 50 questions in 50 minutes — about a minute per question — multiple-choice with answers A to E marked on a separate OMR sheet, and no calculator. Angles usually appear as two or three questions inside the wider maths paper. Because the answer is chosen from five options, teach your child to work out the value first and then find the matching letter, rather than testing each option. That raw score is later converted to a Standard Age Score (SAS, roughly 69–141, with 100 as average and many grammar schools looking for around 111 or above), and the score is age-adjusted so younger children in the year group are not disadvantaged. Angles are equally prevalent in CSSE Essex papers, though there the child usually writes the working rather than picking a letter.
Difficulty progression: Year 5 versus Year 6
The same skill scales up sharply between year groups, which is why the graded tiers matter.
- Year 5 (easier): "Two angles on a straight line are 110° and y. Find y." One rule, one subtraction: 180 − 110 = 70°.
- Year 6 (exam level): "In a diagram, a triangle shares a vertex with a straight line and a pair of vertically opposite angles. Find the missing angle." Three facts chained together, in a diagram that is deliberately cluttered.
Build the ladder deliberately: master single-rule questions, then two-step, then multi-step diagrams. Once a tier is secure, keep it warm inside full timed mock papers rather than more isolated drilling, and use the revision hub to schedule short, spaced sessions.
How to use the worksheets
- Diagnose: one Secure-tier sheet, unaided. Score under 70%? Drop a tier. Over 90%? Climb one.
- Little and often: 15–20 minutes daily beats a weekend marathon — retention lives in the gaps between sessions.
- Review errors out loud: the child explains what went wrong; you resist explaining first. Self-diagnosis sticks.
- Fold into mocks: once a topic hits Greater Depth, let full timed papers keep it warm.
Download free angles worksheets
Every angles worksheet — with answer keys and OMR sheets — is free in our worksheet library under the Maths tab. No card, no email wall. For exam-style application, the mock library and free papers hub carry the same topic inside full papers, and the live leaderboard turns timed practice into a bit of friendly competition.
Frequently asked questions
Is a protractor or calculator allowed in the 11+?
No. GL papers are non-calculator, and angles questions are solved by reasoning with angle facts, not by measuring. Children should learn to find values from the given numbers rather than the picture.
How many angles questions come up?
Usually two or three within the wider maths paper, but the underlying facts also support shape, symmetry and coordinate questions, so the return on mastering them is high.
What year should we start?
Introduce single-rule angle facts in Year 4 or 5, then build multi-step diagram questions through Year 6. Starting the harder chained questions in the autumn of Year 5 leaves comfortable time to reach exam standard.