Discovering the Various Types of Angles: An Introduction to Acute, Obtuse, Right, and More

Table of Contents

What are Angles?

Angles are created when two straight lines or rays unite with each other at the same place. 

The word “angle” originates from the latin word, “angulus” which means corner. The angle is represented by the symbol “∠”.

A protractor is typically used to measure angles and quantify them in degrees. Angles can alternatively be expressed in terms of pi (), or in radians. 

There are two main components of an angle: 

1. Arms

The two rays that intersect at the same location to form the angle are its arms.  

2. Vertex

A vertex is the collective end of the two rays. Node is another name for vertex.

Categories of Angles

Angles can be divided into two categories: 

  1. Depending on the Direction
  2. Depending on the Rotation

5 Types of Angles Based on Direction

1. Acute Angle

An acute angle is an angle which lies in the range of 0 degree to 90 degrees.  

2. Obtuse Angle

An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.

3. Right Angle

90 degrees is the standard length for a right angle.

4. Straight Angle

When measured, a straight angle has a 180-degree angle. Since the angle between its arms is 180 degrees, you can see that it is simply a straight line and results from the intersection of two perpendicular lines.

5. Reflex Angle

A reflex angle is an angle that is greater than 180 degrees but lesser than 360 degrees. 

2 Types of Angles Based on Rotation

1. Positive Angles 

If a ray rotates anticlockwise on a two-dimensional plane, the angle created as a result of the rotation is referred to as a positive angle. An angle is positive if it is drawn in the (+x, +y) plane. 

2. Negative Angles 

If a ray rotates in a clockwise direction, it forms a negative angle. When an angle is drawn from the origin toward the (x, -y) plane, the result is a negative angle. 

Pair of Angles

There are various angles that exist when two angles are paired, namely;

1. Complementary Angles

Two angles that add up to 90 degrees are said to have complementary angles. A frequent occurrence is when they make a right angle. 

2. Supplementary Angles

Two angles that add up to 180 degrees are called supplementary angles. The situation when they are on the same side of a straight line is a typical one.

3. Linear Pair

Linear pairs are formed when the non-common arms of two neighboring angles are direct across from one another or extend in the opposite direction. They clearly form a straight line when referred to as linear. 

4. Adjacent Angles

If two angles share a side and a vertex, they are said to be adjacent. In other words, adjacent angles do not overlap and are placed next to one another immediately. 

5. Vertically Opposite Angles

When two lines cross at a single point (referred to as the vertex), vertical angles, sometimes referred to as vertically opposite angles, are produced on either side of the shared vertex. 

Properties of Angles

1. When two rays emerge from a single place, the figure is said to be an angle. The two rays that make up the angle are referred to as the angle’s arms or sides, and this point is known as the angle’s vertex. 

2. A straight line always has a 180-degree angle on one side.

For instance, ∠a + ∠b + ∠c = 180 degrees.

3. If two opposing angles sum up to 180 degrees, they become a linear pair of angles.

4. A point’s surrounding angles are always added up to 360 degrees. 

For instance, ∠a + ∠b + ∠c + ∠d + ∠e +∠f = 360 degrees.

5. Angles that are greater than 180 degrees but lesser than 360 degrees are known as reflex angles.  

 6. Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal. These are referred to as vertical angles at times.

Exploring the Practical Uses for Different Types of Angles in Real World Situations

1. Architects and Engineers

Angles are used in the design of homes, machinery, structures, roads, and bridges by architects and engineers. 

2. Sports

Athletes perform better when given angles. Angles are important in every sport. In cricket, for instance, the batsman must turn the bat at a specific angle in order to smash the ball and cause it to travel towards the boundary. 

3. Artists and Designers

Artists employ angles when creating portraits in paintings and drawings. Angles are used in clothing design by fashion designers. 

4. Geography and Astronomy

Any location in geography is determined by latitudes and longitudes utilizing angles that are subtended at the Earth’s center. Using angles, astronomers can determine how fast the Earth, other planets, and other celestial bodies rotate. 

FAQ's on Types of Angle

There are 5 types of angles based on direction. These are the most typical sorts of angles used in geometry.

  1. Acute Angle
  2. Obtuse Angle
  3. Right Angle
  4. Straight Angle
  5. Reflex Angle


Straight angle is created by half rotation. It is created by turning one ray 180 degrees in relation to another beam. It changes a point’s direction. It is precisely one-half of a revolution, or one-half of a whole angle. 

Another way to create it is to link two right angles together, as in 90° + 90° = 180°.


A ray that revolves between 90° and 180° around a point creates an angle known as an obtuse angle. As a result, a 120° angle can be an obtuse angle. 


An angle that falls between the ranges of straight angles, or 180° and 360°, is referred to as a reflex angle. Thus, the reflex angle is the largest.

An angle with a measurement of zero degree or zero radian is referred to as a zero angle. When two angle arms lay on top of one another with a common vertex, a zero degree angle is created.  

Conclusion: Understanding the Different Types of Angles and Their Uses Can Help You Solve Problems in Math & Science

Angles are everywhere and are essential to both math and science in our daily lives. 

  • Foods like a slice of pizza, a piece of cake, and nacho chips all contain a triangle. 
  • A pair of scissors is made up of two arms that pivot together. When the scissors are opened, an angle is made on either side. The scissors’ handle on the other arm angles with the bottom of the other arm. 
  • Letters L and V have right angles, 90 degree angles in them. 
  • The clock hands are at an angle to one another. For instance, the clock hands make a straight angle at 3 o’clock. 
  • While performing, even dancers, martial arts artists take angles.