Measure angles with a protractor
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.
The two scales run opposite ways and add to \(180\) at every mark.
| Outer scale | Inner scale |
|---|---|
| \(30^\circ\) | \(150^\circ\) |
| \(70^\circ\) | \(110^\circ\) |
| \(130^\circ\) | \(50^\circ\) |
How to measure an angle
- Place the centre on the vertex and a straight edge along one arm.
- Choose the scale that reads \(0\) on that arm.
- Read where the second arm crosses that scale.
The baseline reads \(0\) on the outer scale, so use it.
The angle is \(30^\circ\), which is acute.
It opens past \(90^\circ\), so a reading over \(90\) is right.
The angle is \(130^\circ\).
Each tick is \(10^\circ\), so halfway is \(5^\circ\) more than \(20\).
The angle is \(25^\circ\).
| \(180-70\) | \(=\) | \(110\) |
The true angle is \(110^\circ\).
Common pitfalls
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.