# Angles – Definition, Parts, Types, FAQs, Examples

Updated on January 14, 2024

The measurement of the amount of rotation or turn that occurs between two lines, rays, or segments is accomplished by using angles, a fundamental mathematical concept. As a result, angles are utilized in a wide range of fields, from construction and engineering to navigation and astronomy, and they are an essential component of geometry, trigonometry, and other mathematical disciplines.

This article will look at the fundamentals of angles, including their definition, symbols, parts, types, measurements, and construction.

## What Are Angles?

A geometric figure called an angle comprises two lines or rays that start from the same point, called the vertex. The arms or sides of an angle are the two lines or rays that make up the angle. The angle is measured in degrees, radians, or other units, depending on the application.

The relative positions and orientations of two lines or objects in space are described using the concept of angles. The rotation between two lines or objects, such as a compass needle turning around a fixed point, can also be measured using angles.

## The Symbol of Angle

An angle’s symbol typically is a small arc with the angle’s vertex at its center and two rays extending from either end of the arc to form the angle’s sides. Typically, the sign is “ABC,” with A, B, and C representing points on the two rays that make up the angle. The letter in the middle of the symbol typically represents the angle’s vertex.

## Parts of Angles

An angle’s three main components are the interior, arms, and vertex.

### Vertex

The angle’s vertex is the point at which the two arms of the angle meet.

### Arms

The arms of the angle are the two lines or rays that make up the angle. The arms of the point can be broadened endlessly in the two headings.

### Interior

The space between the two arms of the point is known as the inside of the point. The area where the measurement of the angle is made is in the interior of the angle.

## Types of Angles

There are several different types of angles, each of which differs in size and position from other angles. The most prevalent angles are:

### Acute angle

An angle less than 90 degrees is called an acute angle. The two arms of the point are near one another. It is otherwise known as a reference angle.

### Right angle

An angle that measures exactly 90 degrees is called a right angle. Put another way, it is the angle bisector of an angle on a straight line.

### Obtuse angle

An angle greater than 90 but less than 180 degrees is known as an obtuse angle. So , the two arms of the point are far separated.

### Angle on a straight line

An angle that measures exactly 180 degrees is called a straight angle. The two arms of the point are collinear.

### Reflex angle

An angle greater than 180 degrees but less than 360 degrees is known as a reflex angle. The angle’s two arms point in opposite directions.

## Interior and Exterior Angles

There are four angles created when two lines meet. Two of these are interior angles, and the other two are exterior angles. The angles inside the polygon created by the intersecting lines are called the interior angles, while those outside are called the exterior angles.

When a polygon has n sides, its interior angles are equal to (n-2) times 180 degrees, while its exterior angles are always equal to 360 degrees.

## Positive & Negative Angles

An angle is said to be positive when measured in the anticlockwise direction, and it is said to be negative when measured in the direction of the clock. Positive points are called direct points, while negative points are called reflex points.

## Angles Based on Rotation

The amount of rotation that separates two lines or objects in space is another way to define an angle. In this instance, the angle is measured in degrees, with 360 degrees representing a complete rotation.

For instance, if we look at a clock face, we see that each hour mark is 30 degrees, and each minute mark is 6 degrees. On the off chance that the moment hand moves from the 12 o’clock position to the 6 o’clock position, it has turned through a point of 180 degrees.

In geometry, points are often estimated as how many times a line or beam turns from its underlying situation to its last position. Most of the time, the unit of measurement is radians, and a full rotation is 2 radians.

## How to Measure an Angle?

Before measuring an angle, we must know how big an angle is in degrees or radians. The measurement can be accomplished in various ways, depending on the circumstances.

### Protractor

An instrument used to measure angles is the protractor. It comprises a level, crescent piece of plastic or metal, with a size of degrees set apart. To utilize a protractor, put the focal point of the protractor on the vertex of the point and adjust one of the arms of the point with no blemish on the scale. Then, use the scale to read the number of degrees for the opposite arm of the angle.

### Trigonometry function

The size of an angle can be determined using trigonometric functions, the double angle formulas, such as sine, cosine, and tangent. Trigonometry extensively uses these functions, double angle identities, which are based on the ratios of the sides of a right triangle.

### Calculator

Most scientific calculators have a function that lets you figure out how big an angle is in degrees or radians. Enter the ratio of the angle’s sides or its decimal or fractional equivalent and press the appropriate button to convert the result to degrees or radians to use this function.

## How to Construct Angles?

In math, points can be built utilizing different strategies, contingent upon the prerequisites of the issue. The most prevalent approaches to creating angles are:

### The use of a protractor

A protractor can be utilized to build a point of a given size. Mark the starting point of the other arm of the angle on a ray drawn from the angle’s vertex to accomplish this. Then, at that point, put the protractor on the beam, with the focal point of the protractor at the vertex of the point, and adjust one of the arms of the point with no blemish on the scale. At last, draw the other arm of the point through the imprint on the beam that compares to the necessary size of the point.

### Using the compass

A compass can divide an angle into two equal parts or create angles of a particular size. Follow these steps to create a given-size angle:

- Draw a beam from the vertex of the point and imprint the beginning stage of the other arm of the point on this beam.
- Put the place of the compass on the vertex of the point and draw a bend that crosses the two arms of the point.
- Place the point of the compass at the point where the two arms meet and draw another arc that intersects the first one without altering its width.
- Draw a straight line from the angle’s vertex to where the two arcs meet. One of the arms with the required angle will be this line.
- Draw a straight line from the angle’s vertex to where the second arc and the ray meet.

### Using a set square

A set square can be utilized to build the right points or different points that are products of a 45 degree angle. To develop a point of a given size, follow these steps:

- Draw a beam from the vertex of the point and imprint the beginning stage of the other arm of the point on this beam.
- Put the set square on the beam, with one edge of the set square lined up with the beam.
- Define a boundary along the other edge of the set square until it crosses the other arm of the point.
- Draw a straight line from the angle’s vertex to the intersection of the other set square edge and the ray.

### Using lines in parallel

Equal lines can be utilized to build points equivalent to relating points. For example, follow these steps to create a given-size angle:

- Mark the point where the line intersects with one of the parallel lines as the angle’s vertex.
- Draw a line from the angle’s vertex to a point on the other parallel line.
- Define a boundary from the place of convergence of the two lines to a point on the other equal line, with the end goal that the two lines structure the expected point.
- Define a boundary from the point’s vertex to the place of convergence of the two lines.

## Frequently Asked Questions on Angles

### What are the six types of angles?

Six types of angles exist:

- Acute angle: a 0 to 90 degree angle.
- Right angle: an angle of precisely 90 degrees.
- Obtuse angle: an angle that lies between 90 to 180 degrees.
- Straight angle: an exact 180-degree angle.
- Reflex angle: an angle measuring from 180 to 360 degrees.
- Whole rotation angle: an angle with an exact 360-degree measurement.

### How are angles measured?

Angles can be measured in degrees by using either a double angle formula of trigonometry or a protractor. A degree corresponds to one-sixth of a circle’s full rotation. By aligning its base with one of the angles’ sides and its center with the angle’s vertex, a protractor can be used to measure angles.

The protractor’s scale is used to determine the angle’s measurement. Geometry includes utilizing the proportions of the sides of a right triangle to compute the points.

### What is the value of an angle equal to 60 degrees in radians?

The following formula converts degrees to radians: radians equal 180 x (degrees). As a result, 60 degrees equals (60 x pi)/180, or pi/3 radians.