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Mathematics · MeasurementMathematics · Geometry

Measuring and constructing angles

How do you draw an exact 60° angle with only a compass and a ruler?

Reading a protractor correctly, measuring and drawing angles, and constructing 60°, 120°, 90°, 30° and 45° angles and bisectors with a ruler and compass.

5 depths≈ 205 min of reading74 practice questions

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  1. Discoverabout 30 minAngles you can measure and makeOpen the geometry box, learn what a degree is, estimate angles by eye, measure and draw angles with a protractor, and discover how a compass alone can make an exact 60° angle.Owner-accepted · not line-by-line reviewed
  2. Understandabout 40 minReading the protractor and the compass constructionsLearn the precise protractor method (and the wrong-scale trap), measure and draw reflex angles, copy lengths with a compass, and construct 60°, 120°, 90°, 30° and 45° angles and perpendicular bisectors with the reason each one works.Owner-accepted · not line-by-line reviewed
  3. Investigateabout 40 minTest it: estimates, radii and angle recipesPredict and test: does arm length matter, what does a wrong-scale reading look like, how good is your eye, does the compass radius matter, which angles can bisecting and set squares reach, how accurate can a check be, and why bisectors always work.Owner-accepted · not line-by-line reviewed
  4. Go deeperabout 45 minWhy the constructions workFind out why each compass construction is exact: equilateral triangles for 60°, congruent triangles for bisectors, equidistant points for perpendiculars. Then test edge cases, measure reflex angles, analyse errors and meet the impossible trisection problem.Owner-accepted · not line-by-line reviewed
  5. Extendabout 50 minTriangles, polygons and the impossible angleConstruct triangles from SSS, SAS and ASA, draw regular polygons from a circle, discover which polygons and whole-degree angles are constructible (multiples of 3°), meet the trisection problem, and use angles in projects, puzzles and careers.Owner-accepted · not line-by-line reviewed

Practise and apply

Question bank · 74 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 15Core 30Stretch 19Challenge 10

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Connected ideas

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

Measuring and constructing angles

  • Builds on

    Angles

    Knowing angle types and pairs tells you what you are measuring and checks if your construction is sensible.

  • Used in

    Shape and space

    Drawing accurate triangles, squares and regular polygons needs measured or constructed angles.

Words to know

63 words are explained in these lessons

All vocabulary →

anglearmvertexdegree (°)right anglestraight angleacute angleobtuse anglereflex anglegeometry boxprotractorcompass+51 more