Angles and their Properties
Angles and their properties
Angles are an important part of geometry that we see all around us. From the corners of a book to the hands of a clock, angles are everywhere in our daily lives. In simple terms, an angle is formed when two lines or rays meet at a point called the vertex.
Angles are measured in degrees (°), and they help us understand the amount of turn or rotation between two lines. They can be of different types, such as acute, right, obtuse, straight, and reflex angles, based on their size.
In this project, we will explore the different types of angles, their properties, and their applications. We will also discuss angle relationships, such as complementary, supplementary, and vertically opposite angles, and examine how these relationships are used in geometry and everyday life.
Parts of Angles
- Vertex- The corner points of an angle is known as Vertex. It is the point where two rays meet.
- Arms– The two sides of angle, joined at a common endpoint.
- Initial Side – It is also known as the reference line. All the measurements are done taking this line as the reference.
- Terminal Side- It is the side (or ray) up to which the angle measurement is done.
Types of Angles
There are different kinds of angles based on their measurement.
Acute Angle: An Acute Angle is an angle whose angle measures less than 90 degrees. Such angles as 60 degrees, 50 degrees, etc. are acute angles.
Right Angle: A Right Angle is an angle that measures exactly 90 degrees. The angle at 90 degrees is always a right angle.
Obtuse Angle: Obtuse Angle is an angle whose angle measures between 90 degrees to 180 degrees. Angles at 120 degrees, 150 degrees, etc. are Obtuse Angles.
Straight Angle: A Straight Angle is an angle whose angle measures exactly 180 degrees. This is called a straight angle.
Reflex Angle: A Reflex Angle is an angle whose angle measures between 180 degrees to 360 degrees. Angles at 200 degrees, 260 degrees, etc. are Reflex Angles.
Complete Angle: A Complete Angle is an angle whose angle measures exactly 360 degrees. This is called a complete angle.
Pair of Angles
Complementary angles: If the sum of the two angles is 180°, they are called complementary angles.
Supplementary angles: If the sum of the two angles is 90°, they are called supplementary angles.
Linear Pair: If the non-common arms of adjacent angles are exactly opposite each other or extend in the other direction, then they are called linear pairs. By linear, it is clear that they form a straight line
Adjacent angles: If two angles are attached to a common arm and have a common vertex, so they are considered adjacent angles, and the non-common arms are on either side of the common arm, too.
Vertically Opposite Angles: The angle created on either side of the common vertex is called vertical angles or vertically opposite angles if both lines converge at a single point (called the vertex).
Properties of Angles
Important properties of the angle are:
For one side of a straight line, the sum of all the angles always measures 180 degrees.
The sum of all angles always measures 360 degrees around a point.
An angle is a figure where, from a common position, two rays appear.
The vertex of the angle is called this point and its arms or sides are called the two rays forming the angle.
A reflex angle is called an angle which is greater than 180 degrees but less than 360 degrees.
They form a linear pair of angles if two opposite angles add up to 180 degrees.
The two opposite pairs of angles formed are called vertically opposed angles where two lines parallel each other.
Conclusion
An angle is a formation of two lines meeting at a common endpoint called the vertex. These angles can either be positive or negative. A positive angle forms from the counterclockwise direction of the rays and a negative angle is formed from the clockwise direction of the rays. Acute Angle, Obtuse Angle, Right Angle, Reflex Angle, Complete Angle, and Straight Angle are the types of Angles. Vertex, Arms, Initial Side, and Reference Side are the parts of an Angle. Now, it is clear what the angle is.
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