Estimate the size of angles
Theory
Estimate an angle by comparing its opening with benchmark turns: half a right angle (\(45^\circ\)), a right angle (\(90^\circ\)), a straight angle (\(180^\circ\)) and a full turn (\(360^\circ\)).
A right angle is a quarter of a full turn, \(360\div 4=90^\circ\); it is the main benchmark.
Half a right angle is \(45^\circ\), a straight angle is \(180^\circ\) and a full turn is \(360^\circ\).
First decide whether the opening is less than, equal to or more than a right angle, then compare with \(45^\circ\).
These benchmark turns are built from the right angle.
| Turn | Degrees |
|---|---|
| Half a right angle | \(45^\circ\) |
| Right angle (quarter turn) | \(90^\circ\) |
| Straight angle (half turn) | \(180^\circ\) |
| Three-quarter turn | \(270^\circ\) |
| Full turn | \(360^\circ\) |
How to estimate an angle
- Compare the opening with a right angle: under, equal or over \(90^\circ\)?
- Compare with \(45^\circ\) to sharpen the estimate.
- Choose the nearest sensible value.
| \(360\div 4\) | \(=\) | \(90\) |
A right angle is \(90^\circ\).
It is less than a right angle and just over half of one.
About \(50^\circ\) is sensible.
| \(4\times 90\) | \(=\) | \(360\) |
A full turn is \(360^\circ\).
| \(90\div 2\) | \(=\) | \(45\) |
Half a right angle is \(45^\circ\).
Common pitfalls
Frequently asked questions
How do you estimate the size of an angle?
Compare its opening with benchmark turns. First check whether it is under or over a right angle (\(90^\circ\)), then compare with \(45^\circ\).
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 \(360^\circ\).
Does the length of the arms change the angle?
No. The angle depends only on how far the arms are spread apart, not on how long they are drawn.
How many degrees is a full turn?
A full turn is \(360^\circ\), which is four right angles. A three-quarter turn is \(270^\circ\) and a half turn is \(180^\circ\).