Angles: The Basic Component of Geometry
Angles are the most important part to be studied in geometry. They form the base of geometry and with the help of their various properties, many complex problems of geometry are solved. It is important to analyze the various properties associated with the angles because they form an integral component of geometry. There are a variety of angles in Mathematics with a wide number of applications. One of the most important applications of angles in trigonometry. The entire idea of trigonometry is based on angles. This indicates the importance of angles. It is critical to study the basics of the different angles and the relationship between all those angles. There are many different types of angles such as the vertical angles, the acute angles, the obtuse angles, the right angle, and many such angles.
To know about the different angles and to study the different properties associated with them is what makes geometry intriguing. An angle is actually a figure that is formed by the intersection of two lines. They can also be formed by the intersection of two respective planes. It is very crucial to study the different angles formed and the relation between those angles when two lines meet. An angle actually describes the rotation of a particular line with respect to another line. One can solve all the complex problems in geometry only after knowing the various relationships between the different angles. This article discusses the different angles and also discusses the relation between them.
Major fundamentals of angles:
Classification depending on the measure of the respective angles:
- Acute angles: Acute angles refer to angles that are smaller than 90 degrees in length.
- Obtuse angle: The obtuse angle is defined as an angle that is more than ninety degrees.
- Right Angle: When the angle between two rays is exactly ninety degrees, it is called a right angle. That angle is known as the correct angle.
- Straight angles: The angle is defined by its name. The straight angle is referred to as that angle whose measure is equivalent to one hundred and eighty degrees.
- Reflex Angles: It accounts for those angles whose respective measure lies in the range of one hundred and eighty to three hundred and sixty degrees.
Classification based on the type of rotation:
- Positive angles: It refers to those angles that rotate in an anti-clockwise direction with respect to a specific line.
- Negative angles: It refers to those angles that rotate in a clockwise direction with respect to a specific line.
Classification based on different pairs:
One must remember the fact that the angles that are equal in the measure are known as congruent angles. The angle pair that is congruent in nature is as follows:
- Vertically opposite angles: It is important to know that the vertically opposite angles are equal in length. It is formed when any two respective lines bisect each other. The angles that oppose each other in this bisection are known as vertically opposite angles.
There are many different angle pairs apart from the vertically opposite angles. They are described below:
- Complementary angles: When the sum of the measure of two respective angles is equal to ninety degrees then the angle pair is said to be complementary in nature.
- Supplementary angles: When the sum of the measure of two respective angles is equal to one hundred and eighty degrees then the respective angle pair is said to be supplementary in nature.
- Alternate exterior angles: When a line transverses two parallel lines then the exterior angles formed are said to be alternate exterior angles.
- Adjacent angles: The angles that have one common arm and common vertex are said to be adjacent angles.
There are many different types of angle pairs other than these like the interior alternate angles, corresponding angles, and many more. This article is an attempt to cover many such angle pairs and develop clarity in the minds of the readers about the different angles. Students can take the help of Cuemath, an online platform designed to solve the doubts of many students related to Coding and Mathematics. It is crucial to study the different types of angles as they are very important in dealing with the complex problems of geometry.