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An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs, and sometimes as the arms of the angle. Angle is one of the basic concepts of geometry. It is a part of every geometric figure be it triangles, quadrilaterals, or polygons and there are various types of angles.
Let’s understand the different types of angles in maths and their properties.
Types of Angles in Maths
The space formed when two rays meet each other at a common point is called an angle. Angles can be classified both on their measurement and the way they are rotated. Based on the measurement, the different types of angles in geometry are
- Acute Angle
- Right Angle
- Obtuse Angle
- Straight Angle
- Reflex Angle
- Full Rotation Angle
1. Acute Angle
An angle that is less than $90^{\circ}$ is an acute angle. When two rays intersect at a vertex, forming an angle that is less than $90^{\circ}$, an acute angle is formed.
Some examples of acute angles are $10^{\circ}$, $15^{\circ}$, $30^{\circ}$, $60^{\circ}$, $75^{\circ}$.
The figure below shows some acute angles.
2. Right Angle
If the angle formed between two rays is exactly $90^{\circ}$ then it is called a right angle or a $90^{\circ}$ angle.
The figure below shows a right angle or a $90^{\circ}$ angle.
3. Obtuse Angle
An angle that is greater than $90^{\circ}$ but less than $180^{\circ}$ is called an obtuse angle. Some examples of obtuse angles are $105^{\circ}$, $120^{\circ}$, $150^{\circ}$, $165^{\circ}$.
The figure below shows some obtuse angles.
4. Straight Angle
As the name suggests, a straight angle is a straight line, and the angle formed between two rays is exactly equal to $180^{\circ}$. At a straight angle, the two rays are opposite to each other. A straight angle can be formed by combining two adjacent right angles or in other words two right angles make up a straight angle.
The figure below shows a right angle or a $180^{\circ}$ angle.
5. Reflex Angle
An angle that is greater than $180^{\circ}$ and less than $360^{\circ}$ is called a reflex angle.
Some examples of obtuse angles are $210^{\circ}$°, $270^{\circ}$°, $300^{\circ}$°, $325^{\circ}$°.
The figure below shows some reflex angles.
6. Full Rotation Angle
A full rotation angle is formed when one of the arms of the angle goes on a complete rotation or makes a $360^{\circ}$.
The figure below shows a right angle or a $360^{\circ}$ angle.
Key Takeaways
| Angle Type | Angle Measure |
| Acute Angle | Greater than $0^{\circ}$ and less than $90^{\circ}$ |
| Right Angle | $90^{\circ}$ |
| Obtuse Angle | Greater than $90^{\circ}$ and less than $180^{\circ}$ |
| Straight Angle | $180^{\circ}$ |
| Reflex Angle | Greater than $180^{\circ}$ and less than $360^{\circ}$ |
| Full Rotation Angle | $360^{\circ}$ |
Practice Problems
- Define the following angles
- Acute angle
- Right angle
- Obtuse angle
- Straight angle
- Reflex angle
- Full rotation angle
- How many right angles make one straight angle?
- How many right angles make one full rotation angle?
- Write True or False
- The sum of two acute angles cannot be an obtuse angle.
- The sum of two obtuse angles is always an obtuse angle.
- The sum of two acute angles cannot be a reflex angle.
- The sum of two obtuse angles is always a reflex angle.
- The sum of two acute angles cannot be a full rotation angle.
FAQs
What are the six different angles in geometry based on measurement?
The six different angles in geometry based on magnitude are Acute angle, Obtuse angle, Right angle, Straight angle, Reflex angle, and Full angle.
What do you mean by zero angle?
When both the arms of an angle overlap each other and measure the angle of $0^{\circ}$, then it is called the zero angle.
Is the obtuse angle and reflex angle the same?
No, an obtuse angle is different from a reflex angle because obtuse lies between $90^{\circ}$ and $180^{\circ}$ but reflex is always more than $180^{\circ}$.
What is a full rotation angle?
When the measure of an angle is equal to $360^{\circ}$, it is called a full rotation angle. A full rotation angle occurs when the other arm makes a complete rotation and returns to the base.
Conclusion
The major basis of geometry is angles. Angles find their application in nearly all types of questions, be it trigonometry to closed shapes. Understanding angles and angle types will help in solving a lot of tricky questions.
Recommended Reading
- How to Construct a Tangent to a Circle(With Steps & Pictures)
- Tangent of a Circle – Meaning, Properties, Examples
- Angles in a Circle – Meaning, Properties & Examples
- Chord of a Circle – Definition, Properties & Examples
- How to Draw a Circle(With Steps & Pictures)
- What is a Circle – Parts, Properties & Examples
- How to Construct a Perpendicular Line (With Steps & Examples)
- How to Construct Parallel Lines(With Steps & Examples)
- How To Construct a Line Segment(With Steps & Examples)
- What are Collinear Points in Geometry – Definition, Properties & Examples
- What is a Transversal Line in Geometry – Definition, Properties & Examples
- What are Parallel Lines in Geometry – Definition, Properties & Examples
- What is Concurrent lines in Geometry – Definition, Conditions & Examples
- What is Half Line in Geometry – Definition, Properties & Examples
- What is a Perpendicular Line in Geometry – Definition, Properties & Examples
- Difference Between Axiom, Postulate and Theorem
- Lines in Geometry(Definition, Types & Examples)
- What Are 2D Shapes – Names, Definitions & Properties
- 3D Shapes – Definition, Properties & Types
