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Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Angles

Measure angles with a protractor

20 practice questions 0 video lessons Theory + worked examples
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Theory

Put the centre of the protractor on the vertex and one arm along the straight edge, then read the scale that starts at zero on that arm. The two scales always add to \(180\).

The vertex is the point where the two arms of the angle meet; the protractor centre sits there.

The straight edge lies along one arm, and that arm is where the measuring starts from.

A protractor has two scales; read the one that shows \(0\) on that arm. An angle under \(90^\circ\) is acute, over \(90^\circ\) is obtuse.

Protractor measuring an angle of 30 degrees 0 180 20 160 40 140 60 120 80 100 100 80 120 60 140 40 160 20 180 0 30°
The baseline arm points right, where the outer scale reads \(0\), so use the outer scale. The second arm crosses at \(30^\circ\).

The two scales run opposite ways and add to \(180\) at every mark.

Outer scaleInner scale
\(30^\circ\)\(150^\circ\)
\(70^\circ\)\(110^\circ\)
\(130^\circ\)\(50^\circ\)
Read from zero. Use the scale that shows \(0\) on the baseline arm; if you read the other, the true angle is \(180\) minus your reading.

How to measure an angle

  1. Place the centre on the vertex and a straight edge along one arm.
  2. Choose the scale that reads \(0\) on that arm.
  3. Read where the second arm crosses that scale.
Example 1 — Acute angle
The arm crosses the outer scale at \(30\). What is the angle?
Solution

The baseline reads \(0\) on the outer scale, so use it.

The angle is \(30^\circ\), which is acute.

Example 2 — Obtuse angle
The opening is past a right angle and the arm reads \(130\). What is the angle?
Solution

It opens past \(90^\circ\), so a reading over \(90\) is right.

The angle is \(130^\circ\).

Example 3 — Between ticks
The arm sits halfway between the \(20\) and \(30\) marks. What is the angle?
Solution

Each tick is \(10^\circ\), so halfway is \(5^\circ\) more than \(20\).

The angle is \(25^\circ\).

Example 4 — Wrong scale
Reading the scale that shows \(180\) on the arm gives \(70\). What is the true angle?
Solution
\(180-70\)\(=\)\(110\)

The true angle is \(110^\circ\).

Common pitfalls

Reading the wrong scale. Use the scale that shows \(0\) on the baseline arm, not the one showing \(180\) there.
Forgetting the scales add to 180. If you read the wrong scale, the true angle is \(180\) minus your reading.
Ignoring the sense-check. An angle narrower than a corner must be under \(90^\circ\); a wider one must be over.

Frequently asked questions

How do you measure an angle with a protractor?

Put the centre on the vertex and one arm along the straight edge, then read where the other arm crosses the scale that starts at \(0\) on the first arm.

Which scale do you read?

The one that shows \(0\) on the arm you lined up. If you read the other by mistake, subtract your reading from \(180\).

Why does a protractor have two scales?

So an angle can be measured from either side. The scales run opposite ways and add to \(180\) at every mark.

How do you know if an angle is acute or obtuse?

An acute angle is less than \(90^\circ\) and an obtuse angle is more than \(90^\circ\). Comparing with a right angle checks the reading.