Profile
Settings
Refer your friends
Sign out
Introduction:
The word “angle” comes from the Latin term angulus, which means “corner,” and is linked to the Greek o (ankylos), which means “crooked, bent,” and the English word “ankle.” Both have the root *ank-, which meaning “to bend” or “bow” in Proto-Indo-European. According to Proclus, an angle must be either a characteristic, a number, or a relationship. An angle is created when two lines intersect at a point. The ‘opening’ between these two rays is measured as a ‘angle.’ The sign is a representation of it. Angles are generally measured in degrees and radians, which are circularity and rotational metrics. Angles occur frequently in our daily lives. Engineers and architects employ angles to design highways, buildings, and sports facilities. Carpus of Antioch utilised the second concept, considering an angle as the interval or space between intersecting lines; while Euclid used the third model, viewing an angle as a departure from a straight line. and are not in a straight line with one another.
Types of Angles and Their Characteristics
There are six main types of angles to consider. Each type of angle has its own unique identity based on angle measurement. Let’s go over each type of angle and its properties one by one.
Acute Angle
An acute angle is one with a length greater than 0° but less than 90°.
The Right Angle
A 90-degree angle is referred to as a right angle. Because it takes the shape of the letter L, a right angle is easily recognized.
Obtuse Angle:
Obtuse angles are those that are fewer than 180 degrees but more than 90 degrees.
A Straight Angle
The angle generated by a straight line is known as a straight angle. In other words, a straight angle is a straight line, and the angle formed by two rays is 180 degrees. The two beams are at a right angle to one another. One straight angle is made up of two right angles. Because its measurement is 180°, a straight angle is one-half of a circle’s turn.
Angle of Reflex
A reflex angle can be defined as the angle that is greater than 180 degrees but less than 360 degrees.
Complete Angle
When the measurement of an angle equals 360°, it is called a full angle.
- A straight line forms straight angle measuring 180 degrees.
- A circle forms an angle of 360 degrees.
Lines
A line is a one-dimensional figure with no breadth that stretches in both directions indefinitely. It is made up of an unlimited number of closely spaced points. The line is called a breadthless length by Euclid. It is represented on a cartesian plane by the linear equation ax + by = c.
Rays
Rays are lines that have one end that is the starting point and the other end that goes to infinity. They go in one direction and don’t come to an end. An angle is formed when two rays are linked end to end.
Line Segment
A line segment is defined as a line having 2 endpoints. A line segment’s length can be determined.
Types of lines:
- Horizontal Line: A-line which is parallel to the x-axis and perpendicular to the y-axis is known as a horizontal line.
- Vertical Line: A-line that is parallel to the y-axis and perpendicular to the x-axis is known as a vertical line.
- Parallel Line: Two lines that never meet each other and run together to infinity are known as parallel lines.
- Perpendicular Lines: Lines that make 90 degrees with each other are known as perpendicular lines.
Properties of the Angles and the Lines
As we’ve seen, there are many distinct types of lines and angles, each with its own set of characteristics. There are, however, some fundamental features of lines and angles that can be explored.
Characteristics of the Line.
- Lines are made up of an endless number of points that are near each other.
- They move forever in both directions.
- They have no depth or thickness and are one-dimensional.
Characteristics of the angle
- A geometrical figure created when two lines intersect in the same plane is called an angle.
- The lines that make up an angle are known as its arms (sides), and the place where they meet is known as the vertex.
Conclusion:
Any collection of finitely many lines partitions the plane into convex polygons (possibly unbounded); this division is known as an arrangement of lines.
An angle is a figure formed by two rays, called the sides of the angle, that share the same endpoint, called the vertex of the angle. Angles formed by two rays are contained in the plane in which they are enclosed. When two planes overlap, angles are created as well. They’re referred to as dihedral angles. Angles formed by rays lying tangent to the curves at their intersection can likewise be defined by two intersecting curves.
