How Many Angles Are There In Maths?

There are five types of angles.

Based on their direction, there are generally five types of angles in mathematics. The most common types of angles used in geometry are these five Acute Angles, Obtuse Angles, Right Angles, Straight Angles and Reflex Angles. The distance between two lines is called an "Angle" when the two lines or rays converge at a single point.

Acute Angle

A form of angle known as an acute angle has a measure greater than 0 and less than 90. An acute angle is depicted in the figure below.

Right Angle

A right angle is a particular angle whose measure is precisely 90 degrees. The right angle is shown in the illustration below.

Obtuse Angle

A type of angle with a measure larger than 90° and less than 180° is called an obtuse angle. The illustration of an obtuse angle is shown below.

Straight Angle

The angle's two rays are either in a straight line with respect to one another or they are inclined by 180 degrees. Here, Angle ABC represents a measure of 180 degrees.

Reflex Angle

The reflex angle is that angle that is larger than 180 degrees and less than 360 degrees. Since the reflex angle is complementary to the acute angle on the other side of the line, it can be determined if the acute angle's measurement is known.

Pair Of Angles

There are two other types of angles in addition to the ones stated above: complementary angles and supplementary angles. Two angles are said to as supplementary if their sum is exactly equal to 180° and complementary if it is equal to 90°.

Linear Pair

Linear pairs are formed when the non-common arms of two adjacent angles are directly opposite from one another or extend in the opposite direction. They form a straight line when referred to be linear.

Adjacent Angles

Adjacent angles are joined by a common arm, share a common vertex, and have non-common arms on either side of the common arm.

Vertical Angles

Vertical angles, also known as vertically opposing angles, are generated when two lines intersect at a single point (known as the vertex). These angles are formed on either side of the common vertex.

Angles Formed By Transversal

A transversal line divides or crosses more than two lines at various points. As a result, there are angles created at the intersection.

Examples

Q1: Which type of angle is given in the below figure?

Ans: The measure is less than 90 degrees, hence it is an acute angle.

Q2: Angle O has a measure of 175°. What classification does Angle O fit into?

Ans: Angle O has a measure that ranges from 90° to 180°. As a result, Angle O is an Obtuse Angle.

Q3: Find the complementary angle of 30°?

Let the complementary angle be x, then

x+30°=90°

x=90°-30°

x=60°

The complementary angle of 30° is 60°.

Q4: Find the supplementary angle of 100°?

Let the supplementary angle be x, then

x+100°=180°

x=180°-100°

x=80°

The supplementary angle of 100° is 80°.