Measure angles and make accurate scale drawings
Align and read a protractor correctly · Scale real lengths into drawing lengths · Distinguish measurement from formal construction
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Ratio and unit conversions
- Angle types
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Align and read a protractor correctly
- Scale real lengths into drawing lengths
- Distinguish measurement from formal construction
Prepare your paper
When a practice task gives numerical input geometry rather than a printed figure, first prepare that source segment, angle, triangle or circle with measuring tools as needed. Then put the measuring scale or protractor aside for the requested formal copying or bisector steps: use a compass and unmarked straightedge to locate the new points. The preparation supplies the givens; it is not a replacement for the formal construction.
The website diagrams explain relationships; their screen size is not a centimetre calibration or a ready-to-measure template. Keep the input figure and useful construction arcs on paper. Your drawing is self-checked and needs human review for reliable marking.
Measure the chosen angle
Place the protractor center at the vertex and its zero line on one arm. Read the scale starting from that zero in the chosen direction. Check whether the answer should be acute, obtuse or reflex; the other numbered scale can give the supplement.
For a reflex angle, measure the smaller turn and subtract from 360° when the task asks for the remaining turn. A thick line or misplaced center reduces precision, so use the accuracy specified by the question.
A scale is a length ratio
At 1:200, 6 m becomes 600 cm/200 = 3 cm on paper. Convert to common units before applying the ratio. A 6–8–10 m triangle can be drawn as a 3–4–5 cm triangle at that scale, using the scaled sides to locate the third vertex.
Use a ruler/protractor when the task requests measurement or a scale drawing. For a formal compass-and-straightedge bisector or copied angle, preserve the exact construction method rather than replacing it with a measured approximation. A drawing can be checked by measurement without changing how it was located.
Sources for this lesson
Pause and explain
At 1:200, how long on paper is a 6 m distance?
Worked example
At scale 1:200, draw lengths representing 6 m, 8 m and 10 m.
Show the worked solution
- Convert to 600, 800 and 1000 cm.
- Divide each by 200.
Answer 3 cm, 4 cm and 5 cm on the drawing.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
The smaller turn between two rays measures 65°. Find the reflex turn.
Give me a hint
Use a complete turn.
Compare my reasoning
- A full turn is 360°.
- 360−65 = 295°.
295°.
Look for these in your work
- Identify the specified turn
- Do not use the straight-angle supplement
At 1:500, find drawing lengths for 15 m and 22 m.
Give me a hint
Convert real lengths to centimetres.
Compare my reasoning
- 1500/500 = 3 cm.
- 2200/500 = 4.4 cm.
3 cm and 4.4 cm.
Look for these in your work
- Convert units before scaling
- Use one common scale
A 1:250 drawing has a 7.2 cm side. Find its real length in metres and explain why measuring a midpoint is not a formal bisector construction.
Give me a hint
Reverse the scale; then distinguish checking from constructing.
Compare my reasoning
- 7.2×250 = 1800 cm = 18 m.
- A formal bisector is located by equal intersecting arcs and their line, not by ruler subdivision.
Real length 18 m; use equal arcs for a formal perpendicular bisector.
Look for these in your work
- Apply the scale direction correctly
- Keep formal construction evidence
Common mistakes
- Choose the protractor scale beginning at the aligned zero.
- Scale ratios compare lengths in matching units.
What can you explain now?
At 1:200, how long on paper is a 6 m distance?
Compare with the explanation
3 cm.
600 cm divided by 200 gives 3 cm.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
At 1:200, how long on paper is a 6 m distance?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.