Drawing and measuring: angles, triangles and scale drawings

Architects, engineers and map makers draw accurately. Here is how to measure angles, draw triangles and use scale drawings.

Practise this lesson free (7 questions)

Using a protractor

Estimate first: acute (less than 90°), obtuse (between 90° and 180°) or reflex (more than 180°).
Put the centre on the vertex and line up 0° with one arm. Count up from that 0°.
A reflex angle: measure the smaller angle, then subtract from 360°.

Drawing triangles

Two sides and the angle between them: draw one side with a ruler, measure the angle with a protractor, then draw the second side.
Three sides: draw one side, then use compasses to draw an arc from each end with the other two lengths. Join to where the arcs cross.
The two shorter sides must add to more than the longest side, or the triangle cannot be drawn.

Scale drawings

A scale such as 1 cm to 2 m means every 1 cm on the drawing is 2 m in real life.
Real length = drawing length × 2 m. Drawing length = real length ÷ 2 m.
A scale of 1 : 50 means real lengths are 50 times the drawing lengths, in the same units.
Worked example

A room is 6 m long and 4.5 m wide. Make a scale drawing using 1 cm to 1.5 m. How big is the rectangle on the drawing?

  1. Length: 6 ÷ 1.5 = 4 cm
  2. Width: 4.5 ÷ 1.5 = 3 cm

Answer: 4 cm by 3 cm

Key idea

Estimate, then measure from the 0° on the arm you lined up. Use compasses for three given sides. Multiply by the scale to get real lengths; divide to get drawing lengths.

Key words
Estimate
An approximate answer, often found by rounding each number to 1 significant figure first.
Vertex
A corner of a shape, where edges or sides meet. The plural is vertices.
Reflex angle
An angle more than 180° but less than 360°.

All KS3 Mathematics key terms and definitions →

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Extra practice

2 more questions

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  1. The smaller angle between two lines is 110°. What is the reflex angle?

    Show the answer

    Answer: 250 °

    360 − 110 = 250°.

  2. A student measures an acute angle and writes 130°. What has most likely gone wrong?

    1. Acute angles cannot be measured
    2. They read the wrong scale: the angle is 50°
    3. The angle is really 310°
    4. The angle is really 230°
    Show the answer

    Answer: They read the wrong scale: the angle is 50°

    An acute angle is under 90°, so 130° is the other scale: 180 − 130 = 50°.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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