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Mathematical terms: the definition of angle: a guide to angle in mathematical research
Angle is an indispensable aspect in mathematical research, especially in geometry. Two rays (or straight lines) starting from the same point or the same endpoint form an angle. The point where two rays intersect is called the vertex. The angle of rotation between two arms or sides measuring an angle, usually in degrees or radians. An angle is defined by its metric system (such as degrees) and does not depend on the length of the angle side.

history of the world

The word "angle" comes from the Latin word "angulus", which means "angle", and is related to the Greek word "ankylοs", which means "bend, bend" and the English word "ankle". Both Greek and English words come from the original Indo-European root "ank-", meaning "bend" or "bow".

Angle type

The accurate measurement of an angle of 90 degrees is called a right angle. An angle less than 90 degrees is called an acute angle. An angle of exactly 180 degrees is called a right angle (this is shown as a straight line). An angle greater than 90 degrees but less than 180 degrees is called an obtuse angle. An angle larger than a right angle and smaller than a circle (180 to 360 degrees) is called a reflection angle. An angle of 360 degrees or equal to a whole circle is called a full angle or a full angle.

For example, a typical roof forms an obtuse angle. The light extends outward to adapt to the width of the house, the vertex is located at the center line of the house, and the open end of the angle is downward. The selected angle must be enough to make the water flow out from the roof easily, but not too close to 180 degrees, so as to avoid the surface being flat enough to accumulate water.

If the roof is built at a 90-degree angle (again, the vertex is located on the center line and the angle is open outwards and downwards), the floor space of the house may be narrower. As the angle measurement decreases, the spacing between rays will also decrease.

Naming angle

Angles are usually named by letters to identify different parts of an angle: the vertex and each ray. For example, the angle BAC identifies an angle with "a" as its vertex. It is surrounded by rays "B" and "C". Sometimes, in order to simplify the naming of angles, it is simply called "Angle A".

Vertical angle and adjacent angle

When two straight lines intersect at a point, four angles are formed, such as "A", "B", "C" and "D".

A pair of mutually diagonal angles formed by two intersecting straight lines are called vertical angles or diagonal angles. Diagonal angles are mirror images of each other. The degree of the angle is the same. These pairs are named first. Because these angles have the same degree, they are considered equal or congruent.

For example, suppose the letter "X" is an example of these four angles. The top of "X" forms a "V" shape, which is called "Angle A". The degree of this angle is exactly the same as the bottom of X, forming a shape called "Angle B". Similarly, the two sides of "X" form ">" and ".

In the same example, "Angle A" and "Angle C" are adjacent to each other, and they share an arm or an edge. Furthermore, in this example, the angles are complementary, which means that each of the two angles is equal to 180 degrees (one of the straight lines that intersect to form four angles). The same is true of "Angle A" and "Angle D".