What is an angle

The angle is a sub-area within a plane

In the mathematics, exactly in the geometry, is a angle precisely defined as the area of ​​two half-lines (rays) that have a common starting point within a plane, but extend from this point in different directions.

• The common starting point of the half-line is the so-called vertex, the half-lines themselves are called the legs of the angle.
• An angle can also be better described as an angle field within a plane, since it describes an area of ​​the plane.
• An angle in space can also be created by rotating a ray when it is rotated around an apex in one direction or the other. The area between the output beam and its position after rotation is called the angle of rotation.

Different types of angles

Angles can be found everywhere in daily life, but the different types are mathematically precisely defined.

• If you have a point P and draw an arc around it, then this has an angular dimension of 360 °. This is a full angle.
• If you hit on one Straight lines around a point P, which is located on the straight line, half a circular arc, this is a straight angle with a dimension of 180 °.
• If two straight lines are perpendicular to one another, they form a so-called right angle of exactly 90 °.
• All those with a dimension smaller than 90 ° are called acute angles.
• If the angle is between 90 ° and 180 °, it is called obtuse.
• Correspondingly, obtuse angles have a dimension which is between 180 ° and 360 °.

Use in math

• For example, angles are used to calculate triangles. It is important to know that the angle within a triangle is always 180 °.
• Each angle has a minor angle. Both together always result in a straight angle.
• Angles are also used in the sine, cosine and tangent theorems to calculate triangles.