Estimate the size of angles
Theory
To estimate an angle, compare it with angles you already know: half a right angle (\(45^\circ\)), a right angle (\(90^\circ\)), a straight angle (\(180^\circ\)) and a full turn (\(360^\circ\)). This Year 5 maths page shows these benchmarks, how to decide whether an angle is a little less or a little more than one of them, and how to spot an estimate that cannot be right.
A right angle is a quarter turn, \(90^\circ\). It is marked with a small square at the vertex.
A straight angle is a half turn, \(180^\circ\): the arms make a straight line. A three-quarter turn is \(270^\circ\) and a full turn is \(360^\circ\).
Useful in-between benchmarks: half a right angle is \(45^\circ\), one third of a right angle is \(30^\circ\), and a right angle and a half is \(135^\circ\).
The size of an angle is the turn between the arms. The length of the arms does not change the angle.
Benchmark angles:
How to estimate an angle
- Compare with a right angle: less, about the same, or more?
- Choose the nearest benchmark (\(45^\circ\), \(90^\circ\), \(135^\circ\), \(180^\circ\)).
- Adjust: a little less or a little more.
- Check the estimate is sensible.
(i) Two right angles
(ii) Three right angles
(iii) Four right angles
| \(2 \times 90\) | \(=\) | \(180^\circ\) |
| \(3 \times 90\) | \(=\) | \(270^\circ\) |
| \(4 \times 90\) | \(=\) | \(360^\circ\) |
(i) \(180^\circ\), a straight angle
(ii) \(270^\circ\)
(iii) \(360^\circ\), a full turn
| \(90 - 15\) | \(=\) | \(75^\circ\) |
A little less than a right angle, so about \(75^\circ\) (anything from \(70^\circ\) to \(80^\circ\) is a good estimate).
| \(180 - 170\) | \(=\) | \(10^\circ\) |
\(170^\circ\): only \(10^\circ\) short of a straight angle.
(i) About two thirds of a right angle
(ii) About half a right angle more than a straight angle
| \(90 \div 3 \times 2\) | \(=\) | \(60^\circ\) |
| \(180 + 45\) | \(=\) | \(225^\circ\) |
(i) \(60^\circ\)
(ii) \(225^\circ\)
| \(90 \div 15\) | \(=\) | \(6\) |
About 6.
No. \(110^\circ\) is more than a right angle. An angle smaller than half a right angle is less than \(45^\circ\), perhaps about \(25^\circ\).
Common pitfalls
Frequently asked questions
What are the benchmark angles?
Half a right angle is \(45^\circ\), a right angle is \(90^\circ\), a straight angle is \(180^\circ\) and a full turn is \(360^\circ\).
How do you estimate an angle?
Compare it with a right angle, then with the nearest benchmark such as \(45^\circ\) or \(180^\circ\), and adjust.
Does a longer arm make an angle bigger?
No. The size of an angle is the amount of turn, not the length of the arms.