A Complete Guide Covering The Different Types Of Angles

Angles are a crucial part of geometry and important to be studied to assist the students’ understanding of geometry. An angle is a geometrical figure that is formed when two rays intersect at a point. 

The two rays in the figure are known as sides of the angle, and the common endpoint is known as the vertex of the angle. The intersection of plane rays as well as curved rays is known as an angle. This blog post discusses different types of angles.

Different types of Angles

It can be said that angles are the first thing to be learned about geometry to understand the entire geometry. A student must realise angles well to make their way easily through geometry and mathematics. 

Angles might seem to be very basic, but they prepare the foundation of the subject, which makes them vital. Learning angles at a deeper level helps students build a strong foundation. There are two components constituted by an angle, as follows:

1. Vertex
2. Side

The two sides can intersect in any possible way to form the vertex of the angle. Based on the intersection, angles are classified into four major types: acute angle, right angle, obtuse angle, and reflex angle. We’ll now discuss these different types of angles in detail and their properties to know them better. 

Acute angle and its properties

An acute angle is an angle that always measures less than 90°. An acute angle can also be formed when a right angle is divided into two parts; by this way, we will have two acute angles. For example, two rays A and B meet at a point O; if the angle formed at O is less than 90°, then it will be termed as an acute angle. 

Properties of  an acute angle:

• The measurement lies between 0° to 90°.
• Acute angles make an acute triangle in which all angles are acute. However, their sum will always be 180°.

As mentioned above, acute angles always measure less than 90°; hence, 30°, 45°, 60° are some of the degrees of acute angles. Pair of scissors we use, open at an acute angle. 

Right angle and its properties

When the two rays of the angle meet at a measure of exactly 90°, the angle is classified as a right angle. No angle measuring less than or greater than 90° can be considered to be a right angle. 

For instance, if there are two rays or sides of the angle named as side A and side B, then the intersection point of  A and B  that can be named O must form a 90° so that ∟AOB can be called a right angle. 

Properties of a right angle:

• The measurement of the point of intersection is always 90°.
• A right-angle makes a right-angle triangle with the other two angles as acute angles.

A standing wall makes a right angle with the floor. 

Obtuse angle and its properties

When the sides of an angle intersect to make an angle that measures more than 90°, it is known as an obtuse angle. The measurement of an obtuse angle has to be more than 90° and less than and 180°. 

Obtuse angles are also said to be opposite angles of acute angles. If an angle has two sides named L and M, then the intersection angle of L and M at the vertex O must be <90° and >180° to make an obtuse angle. 

Properties of an obtuse angle:

• The measurements of the intersection point of two rays lie between 90° and 180°.
• It is greater than the right angle and smaller than the straight angle.
• An obtuse angle makes an obtuse angle triangle which has other two angles as acute angles.

There are several degrees that lie in the range of an obtuse angle, such as 95°, 110°, 120°, 165°, etc. 

The angle between the minute hand and hour hand at 12:20 PM is obtuse. 

Straight angle and its properties

When two rays of an angle lie in opposite directions and make an angle measuring 180°, it is a straight angle. The measurement of a straight angle can’t be less than or more than 180°. 

A straight angle makes a straight line through the vertex of the straight angle; that’s why we call it a straight angle. 

Properties of a Straight angle

• The measurement lies exactly at 180°.
• A straight angle consists of two right angles.
• It’s not possible to make a triangle using a straight angle.

You can see a straight angle in the clock when the time will be 6 o’clock, the hour and minute hand will make a straight angle. 

Reflex Angle and its properties

A reflex angle is an angle that measures more than 180° but less than 360°. A reflex angle can lie anywhere between the range of 180° and 360°. It is more than a half rotation but not a complete rotation. A reflex angle always lies on the opposite side of an acute angle and an obtuse angle. 

If you add any of the acute angles, right angle, and obtuse angle to a straight line or 180°, it will make a reflex angle. 

Properties of a reflex angle

• A Reflex angle is always greater than 180° and smaller than 360°.
• A reflex angle always lies opposite to the acute angle and right angle.
• 180° right angle= reflex angle
• 180° acute angle= reflex angle
• 180° obtuse angle= reflex angle

A hinge joint can never make a reflex angle without being broken. 

Conclusion

Geometry is just like a tree with so many branches; lines and angles are one of them. Above, we read about various angles, their way of formation, their measurement, properties, and where we can see them in real life. 

However, there is a further classification of angles supplementary angles, complementary angles, and other angles formed by them. 

Angles are part and parcel of our day-to-day lives — mechanical engineers use them to construct buildings, athletes use angles to throw Javelin, and more. We can’t ignore the importance of angles in mathematics as well as life.