WHAT ARE THE ELEMENTS OF AN ANGLE? - MATHS - 2025

The elements of an angle are the vertex, which is a common point; and two rays or sides. Geometrically, an angle is the part of the plane that is between two rays that start from a common point.

Rays are understood as those lines that begin at a point and extend indefinitely in one direction. Angles are commonly measured in degrees or radians (π).

The elements of the angle are those that appear in its definition, namely:

- A common point, called vertex.

- Two rays, called sides. Rays are also often called rays.

The formal definition of an angle in geometry says the following: "it is the ratio between the length of the arc of circumference, drawn between two rays, and its radius (distance to the vertex)".

Euclid defined an angle as the inclination between two lines that intersect each other in a plane without both being in a straight line; that is, the lines intersect at a single point.

The 5 main types of angles

All types of angles are present in geometry and are widely used when working with polygons.

According to the measure, the angles are classified into:

1- Treble

They are the angles that measure less than 90 degrees (<90º).

2- Straight

They are angles whose measure is equal to 90 degrees (90º). When an angle is right, the sides that form it are said to be perpendicular.

3- obtuse

They are the angles that measure more than 90 degrees but less than 180 degrees (90º <angle <180º).

4- Plain

They are those angles that measure 180 degrees (180º).

5- Complete or perigonal

They are the angles whose measure is equal to 360 degrees (360º).

Examples of angles

- The name "triangle" is due to the fact that this geometric figure has 3 angles, which are formed by the sides of the triangle and the 3 vertices. Triangles are classified according to the measure of each angle.

- In the hands of a clock you can see how the angles vary. The center of the clock represents the vertex and the hands the sides. If the clock shows 3:00 pm, then the angle formed between the hands is equal to 90º.

If the clock shows 6:00 am, then the angle between the hands is 180º.

- In physics, the use of angles is very important to know how certain forces act on a body, or the inclination with which a projectile must be launched to reach a certain destination.

Observation

Angles are not only formed with two rays or rays. In general they can be formed between two lines. The difference is that in the latter case 4 angles appear.

When you have a situation like the previous one, the definitions of opposite angles by the vertex and supplementary angles appear.

You can also define the angle between curves and surfaces, for which it is necessary to know about tangent lines and tangent planes.

References

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