Types of Angles in Maths – Acute, Obtuse, Right, Straight, Reflex

Types of Angles in Maths – Names, Definition and Examples

Have you ever looked at a building and its shadow on the ground? Ever looked at a clock and seen the hour and minutes, hands pointing towards specific numbers. If you replace all the objects with lines, they will align at a certain degree; that is called an angle.  This blog is for Maths, comprising the topic of Types of Angles. It will help students develop a better understanding of Types of Angles in Maths – Acute angle, Obtuse angle, Right angle, Straight angle, Reflex angle, complementary angles, corresponding angles, supplementary angles etc.

What are the different types of angles?

Types of Angles in Maths : An angle develops when two rays or lines meet at a point, and each angle has a different measure. These angles of different measures can be acute, obtuse, right, reflex, and straight angles. Angle pairs are available in a wide range of forms and sizes. Let us look at the various views in more detail.

Types of angles based on measurement

An angle is the space created when two rays intersect at a common point. Angles are classified based on their measurement and rotational direction. Angles are classified as follows based on their measurement. Using the shapes below for each angle type, try understanding the different angles.

Acute Angle

Acute angles are those that are less than 90 degrees. An acute angle gets formed when two rays intersect at a vertex or a point and produce a less than 90° angle. 20°, 30°, 45°, and 60° are examples of acute angles. Look at the diagram to see that PQR is an acute angle.

Right Angle

A right angle gets formed when the angle formed by two rays is exactly 90°. Because of its specification, it is also called a 90-degree angle.

Since angle AOB is a 90 degree angle, it is called a right angle. A right angle is always denoted by a square between the 2 rays.

Obtuse Angle

An obtuse angle is larger than 90 degrees but less than 180 degrees.

The angle created by the rays PQ and QR in the diagram is obtuse.

110°, 130°, 145°, and 165° are instances of obtuse angles.

Straight Angle

As the name implies, a straight angle is a straight line, wherein the angle generated by two rays is exactly 180°. The two rays are opposite each other at a straight angle. Two neighboring right angles can be combined to produce a straight angle, or two right angles can be combined to form a straight angle. ABC is a 180° angle or a straight angle in the diagram.

Reflex Angle

A reflex angle is an angle that is higher than 180 degrees but less than 360 degrees. DEF is a reflex angle in the diagram. Examples of reflex angles include 210°, 250°, and 310°.

Full Rotation Angle

When one of the angle’s arms rotates completely or 360 degrees, it forms a whole rotation angle. AOB = 360° in the diagram, referred to as a full rotation angle.

Types of angles based on rotation

The next angle type is based on the rotational direction of the angle’s arms. An angle gets formed when two lines intersect and meet at a point. Let us look at the many sorts of angles based on rotation.

Positive Angles

Positive angles are those in which the angle is rotated counter-clockwise or anti-clockwise from the base. A positive angle gets formed when side 1(AB) is rotated in the anti-clockwise direction by an angle, as seen in the figure below.

Negative Angles

Angles that rotate clockwise from the base are called negative angles. A negative angle gets formed when side 1 (DE) is rotated in the clockwise direction by an angle, as seen in the figure below.

Types of Angle Pairs

Two angles get represented as a pair of angles. Let us look at the different angle pairings in geometry.

Adjacent Angles

The following requirements must be met for two angles to be neighboring.

• A common vertex connects two angles.
• A common arm connects two angles.

Complementary Angles

Complementary angles get formed when the total of two angles equals 90 degrees. The two angles can be any size as long as they add up to 90 degrees. The two angles may, for example, be 30° and 60°. One angle is the complement of the other angle in this case.

Supplementary Angles

Supplementary angles get formed when the total of two angles equals 180°. When the two angles are combined, they equal 180 degrees. For example, 180° is a sum of 110° and 70°. As a result, these two angles are supplementary. One angle is a supplement to another angle in this case. The 60° supplement, for example, is (180° – 60°), or 120°.

Alternate Interior Angles

When a line or a transversal passes between two parallel lines, the angles created on opposing sides of the line or transversal are known as alternate internal angles.

Alternate interior angle pair 1:

Alternate interior angle pair 2:

Alternate Exterior Angles

When a line or a transversal passes through two parallel lines, the angles formed at the outer side of the line or transversal are called alternate exterior angles, which are also equal.

Alternate exterior angle pair 1:

Alternate exterior angle pair 2:

Corresponding Angles

When a line or a transversal passes through two parallel lines, the angles that are formed at the same position or on the same side of the transversal are corresponding angles, which are congruent.

Corresponding Angles Pair 1:

Corresponding Angles Pair 2:

Corresponding Angles Pair 3:

Corresponding Angles Pair 4:

Vertical Angles

When two lines intersect each other, the angles opposite to each other are equal and are termed as vertical angles, or, vertically opposite angles.

Vertical Angles Pair 1:

Vertical Angles Pair 2:

FAQs (Frequently Asked Questions)

1. Define Positive and Negative Angles.

Positive angles: Starting at the angle base, the angles are measured counterclockwise (opposite to the direction in which the clock revolves).

Negative angles: Starting from the angle base, these angles get measured in a clockwise direction.

2. What do you mean by the Magnitude of an Angle?

The rotation around the vertex that causes one of the arms to create an angle is known as the magnitude of an angle. The larger the rotation (or gap) between the arms, the bigger the magnitude.

Angles can get classified according to the angle’s measurement.

The types are:

• Acute angle
• Right angle
• Obtuse angle
• Straight angle
• Reflex angle

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