Classify angles (acute, right, obtuse, straight, reflex)
Theory
An angle is named by its size in degrees. Acute is less than 90°, a right angle is exactly 90°, obtuse is between 90° and 180°, straight is exactly 180°, and reflex is more than 180°.
An angle measures an amount of turn, counted in degrees. A full turn is \(360^\circ\).
Angles are named by size: acute is less than \(90^\circ\); a right angle is exactly \(90^\circ\) (the square corner); obtuse is between \(90^\circ\) and \(180^\circ\); a straight angle is exactly \(180^\circ\); and reflex is more than \(180^\circ\) but less than \(360^\circ\).
To classify an angle, compare its size with the two landmarks \(90^\circ\) and \(180^\circ\).
Each name covers a set range of sizes.
| Name | Size |
|---|---|
| Acute | less than \(90^\circ\) |
| Right | exactly \(90^\circ\) |
| Obtuse | between \(90^\circ\) and \(180^\circ\) |
| Straight | exactly \(180^\circ\) |
| Reflex | more than \(180^\circ\), less than \(360^\circ\) |
How to classify an angle
- Read the size of the angle in degrees.
- Compare it with \(90^\circ\) and \(180^\circ\).
- Name it: below \(90^\circ\) acute, at \(90^\circ\) right, between obtuse, at \(180^\circ\) straight, above reflex.
Compare with a right angle: \(50 < 90\).
Less than \(90^\circ\), so it is acute.
Exactly a quarter turn, the square corner.
It is a right angle.
\(90 + 15 = 105\).
Between \(90^\circ\) and \(180^\circ\), so it is obtuse.
\(180 + 40 = 220\).
More than \(180^\circ\), so it is reflex.
Common pitfalls
Frequently asked questions
What is an acute angle?
An acute angle is smaller than a right angle, so it measures less than \(90^\circ\).
Is 90 degrees acute or obtuse?
Neither. Exactly \(90^\circ\) is a right angle. Acute is below \(90^\circ\) and obtuse is above it.
What is the difference between a straight angle and a reflex angle?
A straight angle is exactly \(180^\circ\). A reflex angle is more than \(180^\circ\) and less than \(360^\circ\).
How many degrees are in a right angle?
A right angle is a quarter of a full turn, so \(360 \div 4 = 90\), which is \(90^\circ\).