Last Updated on January 29, 2022 by David Baddeley

In mathematics, when more than two or two rays meet at a single point, an angle is formed. There are various types of angles classified on the basis of measurement, rotation, and pairs. The types of angles classified on the basis of measurement are as follows: obtuse angle, full rotation angle, acute angle, reflex angle, straight angle, and right angle. On the basis of rotation: positive angle and negative angle. We shall learn about these angles in a detailed manner in the coming sections.

## Vertically Opposite Angle

As mentioned above, angles are classified on the basis of measurement, rotation, and pair. The vertically opposite angle comes under the basis of pairs. Whenever two lines meet at a single point vertically opposite angles are formed. There are various properties of vertically opposite angles, some of them are: they are always equal to each other, they can be either complementary (angle of 90 degrees) or supplementary (two angles measuring 180 degrees). and they are always non-adjacent to each other. The angles which are non-adjacent formed due to the intersection of two lines that are straight.

## Angles Based on Measurement

The angles based on measurement basically signify that the degrees of angles such as 90, 180, 270, 45, 60, and so on are noted and therefore classified into various types. In this section, we may cover the types of angles based on their degrees. Some of them are mentioned below:

- A type of angle which measures less than the degree of 90 can be considered as the acute angle. When two rays meet at the vertex, the acute angle is formed. For example, 60 degrees, 45 degrees, 35 degrees, and many more. When you have a pizza of 5 slices, each slice is at an acute angle.
- The angle that exactly measures 90 degrees can be considered as the right angle. Some real-life examples of acute angles are as follows: the clock hand showing 9:30 A.M., edges of a door opened at a certain angle, the corner of a book, etc.
- The angle that exactly measures less than 180 degrees and more than 90 degrees is considered as an obtuse angle. This angle is also known as the ‘stupid angle’. Some examples are 120 degrees, 150 degrees, 110 degrees, etc.
- An angle that exactly measures about 180 degrees is said to be a straight angle. For example, a surface that is flat or a stick that is straight has an angle of 180 degrees.
- A type of angle that measures less than 360 degrees and more than 180 degrees is considered a reflex angle. Some real-life examples of Reflex angle are as follows: a slice of pizza when taken out of the whole part is considered as a reflex angle.
- An angle that exactly forms the angle of 360 degrees can be defined as the full rotation angle. A circle is an example of a full rotation angle as it measures 360 degrees. The wheels of a car are also an example of a full rotation angle.

## Angles Based on Rotation

In the next paragraph, we may deal with the types of angles that are based on rotation. They are classified into two types: positive and negative angles. The following points carry out an analysis of the angles.

- The type of angle which is rotated, either anti-clockwise or counter-clockwise, is considered as the positive angle.
- The type of angle which always rotates clockwise is defined as the negative angle. It is also used in the angles of a pair of vectors in plane geometry.

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