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Ruiya Math Blog · No. 1

Not drawn to scale: what angle diagrams really tell you

The picture may look like it is giving you the answer. But when a question says not drawn to scale, your eyes are not the evidence — the labels and angle facts are.

For Singapore Primary 5, Primary 6 and PSLE-style angle questions

The tiny phrase that changes everything

Trust the facts, not the look of the lines.

A diagram is often there to help you see which lines meet. It is not always an accurate picture of the angle sizes. A wide-looking angle might be 40°, and a narrow-looking angle might be 70°.

An angle diagram that is not drawn to scaleTwo straight lines meet at point O. The wide angle above O is labelled 128 degrees, and the small adjacent angle to its right is labelled x degrees.O128°x°

This sketch is only a map. The lines look almost like a cross, but the question tells us the angle is 128° — so that is the fact we use.

First, translate the words

What does “not drawn to scale” mean?

Do trust

  • • Numbers written on the diagram
  • • Words in the question
  • • Marks that show equal angles or parallel lines
  • • Angle rules you have learned

Do not trust

  • • Whether an angle looks big or small
  • • A ruler measurement from the screen or paper
  • • Your guess from the diagram’s shape
  • • A line that “looks” horizontal or vertical

A simple example

Find x without measuring anything.

The two angles around a straight line are 128° and x°. Find x.

  1. 1

    Name the rule: angles on a straight line add up to 180°.

  2. 2

    Write the equation: 128° + x° = 180°.

  3. 3

    Find the missing angle: x = 180° − 128° = 52°.

Notice that the answer comes from the straight-line rule, not from how the two angles happen to look in the sketch.

A useful habit

Before you solve, ask these three questions.

01

What numbers and markings does the question actually give me?

02

Which angle rule connects these angles?

03

Have I used a fact, or only trusted my eyes?

Try it with Ruiya

Still unsure which rule to use?

Send Ruiya the angle question and ask: “Which facts should I trust in this diagram?” She can help your child start from the given information instead of guessing from the picture.

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