Angles

How much does a door turn when it opens — and how do we measure a turn?

What an angle is, types of angles, angle pairs (complementary, supplementary, linear pairs, vertically opposite) and how to use them to find missing angles.

5 depths≈ 235 min of reading80 practice questions

The ladder

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Every depth is open. Start where it feels interesting — you can always move back.

Discoverabout 35 minAngles are turnsSee an angle as a turn and as two arms meeting at a vertex. Measure turns in degrees (full 360°, half 180°, quarter 90°), sort angles into seven types, turn through N, E, S, W, read angles on a clock and meet angle partners.Owner-accepted · not line-by-line reviewed
Understandabout 45 minNaming, sorting and pairing anglesDefine an angle as two rays with a common vertex, name it with ∠ABC, and use degrees and landmark angles. Pin down the seven types, clock and compass angles, then adjacent, complementary, supplementary, linear-pair, vertically opposite and around-a-point angles.Owner-accepted · not line-by-line reviewed
Investigateabout 45 minIs it always true? Testing angle ideasInvestigate angle estimation, sums of angle types, complement and supplement patterns, linear pairs and their bisectors, crossing lines, clock-hand puzzles, turning walks around shapes and the tear-the-corners experiment, sorting claims into always, sometimes and never.Owner-accepted · not line-by-line reviewed
Go deeperabout 55 minWhy angles behave: proofs, parallels and polygonsWhy a full turn is 360°, how to write a proof with reasons, why vertically opposite angles are equal, the angles made by a transversal on parallel lines and their converses, the triangle and polygon angle sums, bends and zigzags between parallels, and where 180° fails.Owner-accepted · not line-by-line reviewed
Extendabout 55 minAngles at work and playUse |30h − 5.5m| for any clock time, prove and use the exterior angle property, navigate with bearings and runway numbers, meet the radian, see angles in ramps, ladders, bowling and pie charts, and tackle olympiad-style angle chases, projects and open questions.Owner-accepted · not line-by-line reviewed

Practise and apply

Question bank · 80 questions

9 sections from Foundation to Challenge, each with hints and a worked solution — or play a 10-question round for points and stars.

Foundation 20Core 28Stretch 21Challenge 11

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Connected ideas

Follow a connection when you’re curious — some lead into completely different areas.

Angles

Related to
Shape and space
The corners of shapes are angles: a square has four right angles and a triangle's angles add to 180°.
Builds on
Lines, rays and line segments
An angle is two rays that share an end point; intersecting lines make angle pairs.
Helps you understand
Measuring and constructing angles
Knowing angle types and pairs tells you what you are measuring and checks if your construction is sensible.
Used in
Data handling
In a pie chart each slice's angle shows a share of the data: 360° stands for the whole.
Used inanother area
Electricity
A generator's coil turns through 360° every cycle — 50 full turns a second on India's 50 Hz supply.
Usesanother area
Eclipses
Whether an eclipse is total or partial comes down to angles: the Moon's tilted orbit and the apparent size of two discs.

Words to know

69 words are explained in these lessons

All vocabulary →

anglevertexarmraydegree (°)full turnhalf turnquarter turnzero angleacute angleright angleobtuse angle+57 more