Types of Angles: An angle is a geometric figure formed by two rays meeting at a common endpoint. It is measured in degrees or radians. It deals with the relationship of points, lines, angles, and shapes in space. Understanding different types of angles is crucial for solving theoretical problems in geometry.
As we know an angle is a geometrical shape formed by joining two rays at their endpoints and is generally measured in degrees. There are different types of angles in geometry which are mentioned in the article below. We have mentioned various types of angles with diagrams, definitions, and examples below.
What are Angles?
Angles are a mathematical concept used to measure the number of turns between two lines or line segments that meet at a common point. They are typically measured in degrees or radians, and are often represented by the symbol "θ". In Euclidean geometry, an angle is defined as a figure that is formed by two rays (by their intersection).
The rays are known as the sides of the angle and the common point shared by the two rays is known as the vertex of the angle. Angle tells about the rotation and the amount of rotation of a certain parameter. Therefore, in physics, angular displacement and the terms used in the rotation part are concerned with angles.Â
How many Types of Angles are there?
There are various types of angles based on different classifications. The most basic classification is measurement. There are 6 types of angles based on measurement - Acute Angle, Right Angle, Obtuse Angle, Straight Angle, Reflex Angle, and Complete Angle. Other than that, There are positive angles and negative angles.Â
Read More
Here are the types of angles based on different classifications:
Six Types of Angles
Measurement of angles is useful to differentiate types of angles. Based on their measurement, there are six different types of Angles commonly used in Mathematics:
- Acute Angle - Less than 90° at the Vertex
- Right Angle - between 90° and 180°.
- Obtuse Angle - Exactly 90° at the Vertex
- Straight Angle - Exactly 180°
- Reflex Angle - between 180°- 360°
- Complete Angle - 360°
Below is an explanation of each of the different types of angles with their figures:
Acute Angle
When the two rays make any inclination between zero to ninety degrees it is called an Acute angle i.e. 0° < Angle < 90°. The corners of an acute angle triangle, the tip of a pencil, or the point of a star are some examples of acute angles. Here, the angle given below is acute.
Acute Angle DiagramRead More
Right Angle
When the two rays make any inclination of exactly nighty degrees it is called a Right angle i.e. Angle = 90°. You can find it in many everyday objects, like the corners of a book or the edge of a door frame. Here, the angle given below is a right angle.
Right Angle DiagramAlso Read
Obtuse Angle
When the two rays make any inclination of exactly nighty degrees it is called an Obtuse angle i.e. 90° < Angle < 180°. The largest angle of the obtuse angle tangle is a key example of the obtuse angles. Here, the angle given below is a right angle.
Obtuse Angle Diagram
Read More
Straight Angle
When the two rays make any inclination of exactly 180 degrees it is called a Straight angle i.e. Angle = 180°. A straight angle is used to straight edge which is used to align something parallel to the horizontal. Here, the angle given below is a straight angle.
Straight Angle DiagramAlso Read
Reflex Angle
When the two rays make any inclination of greater than 180 degrees but less than 270 degrees. It is called a reflexive angle i.e. 180° < Angle < 270°. The exterior angle of any basic regular polygon is a reflex angle. Here, the angle given below is a reflexive angle.
Reflex Angle DiagramAlso Read
Complete Angle
When the two rays make any inclination of 360° i.e. they overlap each other. It is called a complete angle i.e. Angle = 360°. Here, the angle given below is a complete angle.
Complete Angle DiagramAlso Read
Types of Angles based on Rotation
On the basis of measurement of rotation, Angle can be two types:
- Positive Angles
- Negative Angles
Positive Angles
Angles that are measured in a counterclockwise direction from the base are called Positive angles. Generally, positive angles are used to represent angles in geometry. From the origin, if an angle is drawn in the First Quadrant, it forms a positive angle.
Negative Angles
Angles that are measured in a clockwise direction from the base are called Negative angles. From the origin, if an angle is drawn in the Third Quadrant, it forms a negative angle.
Positive and Negative AngleTypes of Pair of Angles
Based on the sum of pairs, two angles pairs can be classified asÂ
- Adjacent Angles
- Linear Pair
- Vertically Opposite Angles
- Complementary Angles
- Supplementary Angles
Adjacent Angles
Two angles are called adjacent angles if they share only one common arm. In other words, adjacent angles are those two angles that have a common vertex and a common side but no common interior points. The sum of adjacent angles is equal to the measure of the larger angle formed by the two adjacent angles.
Adjacent Angles DiagramRead
Linear Pair
A linear pair refers to a pair of adjacent angles whose non-common sides are opposite rays. In other words, two angles are said to form a linear pair if their sum is equal to 180°. For example, angles 70° and 110° form a linear pair because they are adjacent angles (share a common vertex and side) and their non-common sides form a straight line.
Linear Pair of anglesMust Read
Vertically Opposite Angles
Vertically opposite angles are a pair of angles formed when two lines intersect. These angles have the same measure, and their opposite rays form a straight line. Vertically opposite angles are always congruent, and the measure of one angle can be used to find the measure of the other angle.
Read More
Complementary and Supplementary Angles
In addition to the types mentioned earlier, there are two more kinds of angles: complementary angles and supplementary angles.
Complementary Angles
If the sum of two angles is equal to 90°, they are termed complementary angles. Two angles are complementary if they sum up to 90°. For example, 40° and 50° are complementary angles as 40° + 50° = 90°. Here, one angle complements the other angle.
Supplementary Angles
If the sum of two angles is equal to 180°, they are termed supplementary angles. Two angles are supplementary if they sum up to 90°. For example, 140° and 40° are supplementary angles as 140° + 40° = 180°. Here, one angle supplements the other angle.
Parts of an Angle
The two main parts related to an angle are - the arms and the vertex.
Parts of an AngleArms of the Angle: The two rays which join at a common point to form the angle are called the arms of the angle. Observe the figure above which shows that OA and OB are the arms of the angle AOB.
Vertex of the Angle: Vertex is a common endpoint that is shared by the two rays. Observe the figure in which the vertex O is marked as the joining point of the two arms.
People Also View:
Solved Examples on Types of Angles
Example 1: An Angle A measures 135° in measure. Which type of category does Angle A fall into?
Answer:Â
Angle A lies between 90° to 180° in measure. Angle A is, therefore, an Obtuse Angle.
Example 2: An Angle S measures 35° in measure. Which type of category does Angle S fall into?
Answer:Â
Angle S lies between 0° to 90° in measure. Angle S is therefore an Acute Angle.
Example 3: An Angle X measures 235 degrees in measure. Which type of category does Angle X fall into?
Answer:Â
Angle X lies between 180° to 360° in measure. Angle X is therefore a Reflex Angle.
Example 4: An Angle Z measures 335° in measure. Which type of category does Angle Z fall into?
Answer:Â
Angle Z lies between 180° to 360° in measure. Angle Z is therefore a Reflex Angle.
Example 5: Find the complement of 40° and the supplement of 25°.
Solution:
Those  angles that sum up to 90°are called as Complementary angles .Â
The complement of 40° is 50° because (90° - 40° = 50°).
Those  angles that sum up to 180°are called as Supplementary angles.Â
The supplement of 25° is 155° because (180° - 25° = 155°).
Important Maths Related Links:
Practice Problems on Types of Angles
1. Identify the type of angle that measures exactly 90 degrees.
Options: A) Acute B) Right C) Obtuse D) Reflex
2. Which type of angle measures more than 180 degrees but less than 360 degrees?
Options: A) Acute B) Right C) Reflex D) Straight
3. If an angle measures 35 degrees, what type of angle is it?
Options: A) Acute B) Right C) Obtuse D) Reflex
4. Which angle is formed by the hands of a clock at 6:00?
Options: A) Acute B) Right C) Obtuse D) Straight
5. A skateboard ramp forms an angle of 175 degrees where it meets the ground. What type of angle is this?
Options: A) Acute B) Right C) Obtuse D) Reflex
Similar Reads
CBSE Class 9 Maths Revision Notes
CBSE Class 9th Maths Revision Notes is an important phase of student’s life when they’re at a turning point in their life. The reason being class 9 is the foundation level to succeed in class 10. As you know, students must complete Class 9 in order to sit for Class 10 board examinations. Also, it la
15+ min read
Chapter 1: Number System
Number System in Maths
Number System is a method of representing numbers on the number line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Let's learn about the number system in detail, including its types, and conversion.Number System in MathsNumber system in Maths is
13 min read
Natural Numbers | Definition, Examples & Properties
Natural numbers are the numbers that start from 1 and end at infinity. In other words, natural numbers are counting numbers and they do not include 0 or any negative or fractional numbers.Here, we will discuss the definition of natural numbers, the types and properties of natural numbers, as well as
11 min read
Whole Numbers - Definition, Properties and Examples
Whole numbers are the set of natural numbers (1, 2, 3, 4, 5, ...) plus zero. They do not include negative numbers, fractions, or decimals. Whole numbers range from zero to infinity. Natural numbers are a subset of whole numbers, and whole numbers are a subset of real numbers. Therefore, all natural
10 min read
Prime Numbers | Meaning | List 1 to 100 | Examples
Prime numbers are those natural numbers that are divisible by only 1 and the number itself. Numbers that have more than two divisors are called composite numbers All primes are odd, except for 2.Here, we will discuss prime numbers, the list of prime numbers from 1 to 100, various methods to find pri
12 min read
Rational Numbers
Rational numbers are a fundamental concept in mathematics, defined as numbers that can be expressed as the ratio of two integers, where the denominator is not zero. Represented in the form p/q​ (with p and q being integers), rational numbers include fractions, whole numbers, and terminating or repea
15+ min read
Irrational Numbers- Definition, Examples, Symbol, Properties
Irrational numbers are real numbers that cannot be expressed as fractions. Irrational Numbers can not be expressed in the form of p/q, where p and q are integers and q ≠0.They are non-recurring, non-terminating, and non-repeating decimals. Irrational numbers are real numbers but are different from
12 min read
Real Numbers
Real Numbers are continuous quantities that can represent a distance along a line, as Real numbers include both rational and irrational numbers. Rational numbers occupy the points at some finite distance and irrational numbers fill the gap between them, making them together to complete the real line
10 min read
Decimal Expansion of Real Numbers
The combination of a set of rational and irrational numbers is called real numbers. All the real numbers can be expressed on the number line. The numbers other than real numbers that cannot be represented on the number line are called imaginary numbers (unreal numbers). They are used to represent co
6 min read
Decimal Expansions of Rational Numbers
Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. So in this article let's discuss some rational and irrational numbers an
6 min read
Representation of Rational Numbers on the Number Line | Class 8 Maths
Rational numbers are the integers p and q expressed in the form of p/q where q>0. Rational numbers can be positive, negative or even zero. Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the righ
5 min read
Operations on Real Numbers
Real Numbers are those numbers that are a combination of rational numbers and irrational numbers in the number system of maths. Real Number Operations include all the arithmetic operations like addition, subtraction, multiplication, etc. that can be performed on these numbers. Besides, imaginary num
9 min read
Rationalization of Denominators
Rationalization of Denomintors is a method where we change the fraction with an irrational denominator into a fraction with a rational denominator. If there is an irrational or radical in the denominator the definition of rational number ceases to exist as we can't divide anything into irrational pa
8 min read
Nth Root
Nth root of unity is the root of unity when taken which on taking to the power n gives the value 1. Nth root of any number is defined as the number that takes to the power of n results in the original number. For example, if we take the nth root of any number, say b, the result is a, and then a is r
6 min read
Laws of Exponents for Real Numbers
Laws of Exponents are fundamental rules used in mathematics to simplify expressions involving exponents. These laws help in solving arithmetic problems efficiently by defining operations like multiplication, division, and more on exponents. In this article, we will discuss the laws of exponent for r
6 min read
Chapter 2: Polynomials
Polynomials in One Variable | Polynomials Class 9 Maths
Polynomials in One Variable: Polynomial word originated from two words “poly†which means “many†and the word “nominal†which means “termâ€. In maths, a polynomial expression consists of variables known as indeterminate and coefficients. Polynomials are expressions with one or more terms with a non-z
7 min read
Polynomial Formula
The polynomial Formula gives the standard form of polynomial expressions. It specifies the arrangement of algebraic expressions according to their increasing or decreasing power of variables. The General Formula of a Polynomial:f(x) = an​xn + an−1​xn−1 + ⋯ + a1​x + a0​Where,an​, an−1​, …, a1​, a0​ a
5 min read
Types of Polynomials (Based on Terms and Degrees)
Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2n
9 min read
Zeros of Polynomial
Zeros of a Polynomial are those real, imaginary, or complex values when put in the polynomial instead of a variable, the result becomes zero (as the name suggests zero as well). Polynomials are used to model some physical phenomena happening in real life, they are very useful in describing situation
13 min read
Factorization of Polynomial
Factorization in mathematics refers to the process of expressing a number or an algebraic expression as a product of simpler factors. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, and we can express 12 as 12 = 1 × 12, 2 × 6, or 4 × 3.Similarly, factorization of polynomials involves expre
10 min read
Remainder Theorem
The Remainder Theorem is a simple yet powerful tool in algebra that helps you quickly find the remainder when dividing a polynomial by a linear polynomial, such as (x - a). Instead of performing long or synthetic division, you can use this theorem to substitute the polynomial and get the remainder d
8 min read
Factor Theorem
Factor theorem is used for finding the roots of the given polynomial. This theorem is very helpful in finding the factors of the polynomial equation without actually solving them.According to the factor theorem, for any polynomial f(x) of degree n ≥ 1 a linear polynomial (x - a) is the factor of the
10 min read
Algebraic Identities
Algebraic Identities are fundamental equations in algebra where the left-hand side of the equation is always equal to the right-hand side, regardless of the values of the variables involved. These identities play a crucial role in simplifying algebraic computations and are essential for solving vari
14 min read
Chapter 3: Coordinate Geometry
Chapter 4: Linear equations in two variables
Linear Equations in One Variable
Linear equation in one variable is the equation that is used for representing the conditions that are dependent on one variable. It is a linear equation i.e. the equation in which the degree of the equation is one, and it only has one variable.A linear equation in one variable is a mathematical stat
7 min read
Linear Equation in Two Variables
Linear Equation in Two Variables: A Linear equation is defined as an equation with the maximum degree of one only, for example, ax = b can be referred to as a linear equation, and when a Linear equation in two variables comes into the picture, it means that the entire equation has 2 variables presen
9 min read
Graph of Linear Equations in Two Variables
Linear equations are the first-order equations, i.e. the equations of degree 1. The equations which are used to define any straight line are linear, they are represented as, x + k = 0; These equations have a unique solution and can be represented on number lines very easily. Let's look at linear e
5 min read
Graphical Methods of Solving Pair of Linear Equations in Two Variables
A system of linear equations is just a pair of two lines that may or may not intersect. The graph of a linear equation is a line. There are various methods that can be used to solve two linear equations, for example, Substitution Method, Elimination Method, etc. An easy-to-understand and beginner-fr
8 min read
Chapter 5: Introduction to Euclid's Geometry
Chapter 6: Lines and Angles
Chapter 7: Triangles
Triangles in Geometry
A triangle is a polygon with three sides (edges), three vertices (corners), and three angles. It is the simplest polygon in geometry, and the sum of its interior angles is always 180°. A triangle is formed by three line segments (edges) that intersect at three vertices, creating a two-dimensional re
13 min read
Congruence of Triangles |SSS, SAS, ASA, and RHS Rules
Congruence of triangles is a concept in geometry which is used to compare different shapes. It is the condition between two triangles in which all three corresponding sides and corresponding angles are equal. Two triangles are said to be congruent if and only if they can be overlapped with each othe
9 min read
Theorem - Angle opposite to equal sides of an isosceles triangle are equal | Class 9 Maths
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Exampl
4 min read
Triangle Inequality Theorem, Proof & Applications
Triangle Inequality Theorem is the relation between the sides and angles of triangles which helps us understand the properties and solutions related to triangles. Triangles are the most fundamental geometric shape as we can't make any closed shape with two or one side. Triangles consist of three sid
8 min read
Chapter 8: Quadrilateral
Angle Sum Property of a Quadrilateral
Angle Sum Property of a Quadrilateral: Quadrilaterals are encountered everywhere in life, every square rectangle, any shape with four sides is a quadrilateral. We know, three non-collinear points make a triangle. Similarly, four non-collinear points take up a shape that is called a quadrilateral. It
9 min read
Quadrilaterals
Quadrilateral is a two-dimensional figure characterized by having four sides, four vertices, and four angles. It can be broadly classified into two categories: concave and convex. Within the convex category, there are several specific types of quadrilaterals, including trapezoids, parallelograms, re
12 min read
Parallelogram | Properties, Formulas, Types, and Theorem
A parallelogram is a two-dimensional geometrical shape whose opposite sides are equal in length and are parallel. The opposite angles of a parallelogram are equal in measure and the Sum of adjacent angles of a parallelogram is equal to 180 degrees.A parallelogram is a four-sided polygon (quadrilater
10 min read
Rhombus: Definition, Properties, Formula and Examples
A rhombus is a type of quadrilateral with the following additional properties. All four sides are of equal length and opposite sides parallel. The opposite angles are equal, and the diagonals bisect each other at right angles. A rhombus is a special case of a parallelogram, and if all its angles are
6 min read
Trapezium: Types | Formulas |Properties & Examples
A Trapezium or Trapezoid is a quadrilateral (shape with 4 sides) with exactly one pair of opposite sides parallel to each other. The term "trapezium" comes from the Greek word "trapeze," meaning "table." It is a two-dimensional shape with four sides and four vertices.In the figure below, a and b are
8 min read
Square in Maths - Area, Perimeter, Examples & Applications
A square is a type of quadrilateral where all four sides are of equal length and each interior angle measures 90°. It has two pairs of parallel sides, with opposite sides being parallel. The diagonals of a square are equal in length and bisect each other at right angles.Squares are used in various f
5 min read
Kite - Quadrilaterals
A Kite is a special type of quadrilateral that is easily recognizable by its unique shape, resembling the traditional toy flown on a string. In geometry, a kite has two pairs of adjacent sides that are of equal length. This distinctive feature sets it apart from other quadrilaterals like squares, re
8 min read
Properties of Parallelograms
Properties of Parallelograms: Parallelogram is a quadrilateral in which opposite sides are parallel and congruent and the opposite angles are equal. A parallelogram is formed by the intersection of two pairs of parallel lines. In this article, we will learn about the properties of parallelograms, in
9 min read
Mid Point Theorem
The Midpoint Theorem is a fundamental concept in geometry that simplifies solving problems involving triangles. It establishes a relationship between the midpoints of two sides of a triangle and the third side. This theorem is especially useful in coordinate geometry and in proving other mathematica
6 min read
Chapter 9: Areas of Parallelograms and Triangles