Angles and Its Measurement
Basics of Geometry of Class 6
In geometry, there are a different types of angles based on measurement. The names of the basic angles are Acute angle, Obtuse angle, Right angle, Right angle, reflection angle, and full rotation. An angle is a geometric shape that joins two rays at their endpoints. Angle is usually measured in degrees.
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There are a different types of angles in geometry. Angles form a fundamental part of geometry in mathematics. These basics eventually lead to creating more complex geometric figures and shapes.
What is an Angle?
When the two rays meet at a common endpoint and form an angle. The two components of an angle are the "sides" and the "vertex." The side can be categorized into terminal sides and initial sides (or vertical sides) as shown in the image below.
These two rays can combine in a number of ways to create different types of angles in mathematics. Let's begin by studying these different types of angles in geometry.
Parts of Angle
- Arms – Two linear line segments form a vertex.
- Vertex – Point where the arms meet.
- Angle – If the ray is rotated about its endpoint, the measure of its rotation is called the angle between its initial position and final position.
Types of Angles
In mathematics, there are different types of angles based on their direction. These five angle types are the most common ones used in geometry. These are:
- Straight Angles
- Right Angles
- Acute Angles
- Reflex Angles
- Obtuse Angles
- Full Rotation
Straight angle
A straight angle is 180 degrees when it's measured. The image above shows a straight angle or a 180-degree angle. You can see that it's just a straight line because the angle between its arms is 180 degrees.
Right Angle
A right angle is equal to 900. An angle less than 90 degrees is acute, while any angle greater than 90 degrees is obtuse. The image above shows a right angle or a 90-degree angle.
Acute angle
An acute angle lies between the 0 and 90 degrees, or an acute angle is less than 90 degrees. The figure above illustrates an acute angle.
Obtuse angle
An obtuse angle is an opposite angle of an acute. It is the angle which lies between the 90 and 180 degrees or an obtuse angle is greater than 90 degrees and also less than 180 degrees. The above figure illustrates an obtuse angle.
Reflex Angle
Since the measurement is less than 90 degrees, the arms form an acute angle. But what about the angle on the other side? What is the name of the larger angle that is complementary to the acute angle? This is called the angle of reflection. The image below shows the reflex angle.
Any angle whose magnitude is greater than 180 degrees but less than 360 degrees (which is equal to 0 degrees) is a reflection angle.
Full rotation
An angle equal to 360 degrees is called a full rotation or full angle. It occurs when one of the arms turns completely to form an angle.
Types of angles Based on Rotation
- Positive angle: Positive angles are those angles that is measured in counterclockwise from the base. In most cases, positive angles are used to represent angles in geometry. From the origin, if the angle is drawn in the plane (+x, +y), it forms a positive angle.
- Negative angle: Negative angles are those angles that are measured clockwise from the base. From the origin, if an angle is drawn towards the (x, -y) plane, it forms a negative angle.
Pair of Angles
When two angles are paired, then their different angles exist, such as
- Supplementary angles
- Complementary angles
- Linear Pair
- Adjacent angles
- Vertically Opposite angles
Supplementary Angles and Complementary Angles
Apart from the above types, there are two more types of angles which are supplementary angles and Complementary angles. The sum of angles is equal to 90°, then they are called complementary angles and if the sum is equal to 180 degree, then they are called supplementary angles.
Linear Pair
The non-common arms of an adjacent angle are exactly opposite to each other or extend in opposite directions then they are called linear pairs. It is clear to linear that they form a straight line.
Adjacent Angles
When two angles are joined by one common arm and have one common vertex, and also the non-common arm are on the either side of the common arm, then they are called adjacent angles.
Vertical Angles
When the two lines intersect at a single point (called a vertex), then the angle formed on another side of the common vertex is known as vertical angles or vertically opposite angles.
Angles Formed By Transversal
A line that intersects or cuts two or more lines at different points is known as transversal. It is; therefore, there are angles formed at the point of intersection. They are:
- Exterior angles
- Interior angles
- Pairs of Corresponding angles
- Pairs of Alternate interior angles
- Pairs of interior angles
- Pairs of Alternate exterior angles
Frequently Asked Question (FAQs)
Q1. What is reflex angle?
Ans. It is an angle that measures more than 180° and is less than 360°. For example, 270° is a reflex angle.
Q2. How are angles formed?
Ans. An angle is formed when the two straight lines or rays meet at the same endpoint. The common point of contact is known as the vertex of an angle. The term angle comes from the Latin word 'angulus,' meaning "corner."
Q3. Which kind of angle is the smallest?
Ans. The smallest angle is 1 and smaller than a right angle, so we call this an acute angle.
Q4. Which kind of angle is the largest?
Ans. It is an angle that lies between the intervals of straight angles, 180° and 360°.
Q5. Who invented angle?
Ans. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who viewed it as the interval or space between the intersecting lines; Euclid adopted the third concept.
