There are six main categories of angles:

Acute Angle: An acute angle is defined as one that is less than 90 degrees, or as one that falls between 0 and 90 degrees. (0° to 90°)

Obtuse Angle: The reverse of an acute angle is called an obtuse angle. An obtuse angle is one that is larger than 90 degrees and less than 180 degrees, or it is the angle that falls between 90 and 180 degrees. (90° to 180°)

Right Angle: Ninety degrees is the equal of a right angle. A right angle is one that is precisely equal to ninety degrees. (90°)

Linear Angle: When measured, a straight angle is 180 degrees. A 180degree or straight angle is depicted in the above figure. (180°)

Angle of Reflex: The arms make an acute angle because this measurement is less than 90 degrees. However, what about the opposite side’s angle? What is the name of the wider angle that complements the acute angle? We refer to it as a reflex angle. Reflex angles are any angles with measures that are more than 180 degrees but less than 360 degrees, or 0 degrees. (180° to 360°)

Whole Rotation: Full rotation, or full angle, is defined as an angle that is equal to 360 degrees. (360°)
12 Different Kinds of Angles
Now let’s examine the 12 different kinds of angles with examples:

Acute Angle: An acute angle is one that is smaller than ninety degrees. (0° to 90°)

Right Angle: A right angle is one that is precisely 90 degrees. (90°)

Obtuse Angle: An obtuse angle is one that has a measure of less than 180 degrees but more than 90 degrees. (90° to 180°)

Straight Angle: A straight angle is one that is precisely 180 degrees. (180°)

Reflex Angle: An angle that measures more than 180 degrees but less than 360 degrees is called a reflex angle. (180° to 360°)

Full Angle: A full angle is one whose measurement is precisely 360 degrees. (360°)
4 Primary Angles
Let’s examine the four primary angles:

Right Angle: An angle that measures precisely ninety degrees is called a right angle. (90°)

Straight Angle: Any angle with a measure of precisely 180° is considered a straight angle. (180°)

Acute Angle: Angles with a measure of less than 90° are known as acute angles. (0° to 90°)

Obtuse Angle: Angles that measure more than 90° but less than 180° are referred to as obtuse angles. (90° to 180°)
Various Types of Angles
Based on their direction, there are primarily five types of angles in mathematics. The most often used angle types in geometry are these five. These are the following:

Sharp Angles

Stubborn Angles

Appropriate Angles

Linear Angles