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

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July 25, 2022
Types of Angles in Maths – Acute, Obtuse, Right,
Straight, Reflex
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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.

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Acute Angle PQR
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.

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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.

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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.

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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

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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.

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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:

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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.

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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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