We explain what an angle is, its types and characteristics. Also, addition, subtraction, multiplication and division with angles and how to measure them.
What is angle?
Angle is the portion of the plane between two rays (sides) with a common origin called the vertex. The angles start from a point and have two lines that leave from that point and that generate an opening represented by an arc. The degree of opening of these arches (and not their extension) is represented by the angle.
The concept of angle corresponds to geometry, one of the branches of the math, but it also applies in other fields such as engineering, the optics wave astronomy.
The measurement of the angles is carried out from the sexagesimal system that is expressed in degrees (º), minutes (’) and seconds (’ ’). One degree equals 60 minutes and one minute equals 60 seconds. The number of degrees can be up to 360, which is considered the complete turn of a circle. For example: In the hand watch, the hands form angles. At 12 o'clock, when the two hands point to the same side, the angle is 0 °; at 3 o'clock 90 °; at 6 o'clock at 180 ° and at 9 o'clock at 270 °.
Angles are represented by a magnitude that can be analyzed and compared with others, so there are operations between angles. You can add and subtract angles from each other or multiply and divide them by whole numbers.
The line that divides an angle into two equal parts is called the bisector and any point on it equidistant from both sides of the angle.
Types of angles
Angles can be classified according to certain criteria.
According to its amplitude:
- Null angle. It is the one that measures 0 °.
- Acute angle. It is the one that measures between 0 ° and 90 °.
- Right angle. It is the one that measures 90 °.
- Obtuse angle. It is the one that measures between 90 ° and 180 °.
- Flat angle. It is the one that measures 180º.
- Concave angle. It is the one that measures more than 180 °.
- Full angle. It is the one that measures 360 °.
According to the relationship with another angle:
- Supplementary angles. They are angles that add up to 180º.
- Complementary angles. They are angles that add up to 90 °.
According to your position:
- Consecutive angles. They are angles that share a side and a vertex.
- Adjacent angles. They are consecutive angles and the side that they do not share is part of the same line.
- Opposite angles by the vertex. They are angles that share the vertex but none of the sides.
Angles operations
- Sums between angles. When two or more angles are added, the degrees (and also the minutes and seconds if applicable) of each of the angles must be added. For example:
angle α + angle β = angle γ
90º + 70º = 160º - Subtraction between angles. When two or more angles are subtracted, the degrees (and also the minutes and seconds if applicable) must be subtracted from each of the angles. For example:
angle γ - angle β = angle α
160º – 70º = 90º - Multiplications with angles. When an angle is multiplied by a natural number, the degrees, minutes and seconds must be multiplied by that number. In the event that the values of the minutes or seconds exceed 60, these units must be transferred to the following scale. For example:
angle α = 40º 10 ’20”
angle α x 2 = 40º x 2 + 10 ’x 2 + 20” x 2 = 80º 20 ’40” - Divisions with angles. When dividing an angle by a natural number, the degrees, minutes, and seconds must be divided by that number. At the beginning, the degrees are divided by the number and the remainder that is obtained is transformed into minutes (by multiplying it by 60) and is added to the minutes that were already had. The minutes are divided and the remainder is added to the seconds that already had to be divided later.
How do you measure an angle?
To measure the width of an angle, you need a measuring instrument called a protractor. The protractor is graduated, can be circular or semicircular and is usually of plastic. The steps to measure an angle are:
- 1. The center of the protractor, which is usually indicated by a groove, should be placed at the vertex of the angle (the origin of the angle).
- 2. Then it must be verified that one of the sides of the angle coincides with the base of the protractor.
- 3. The graduation of the remaining side is marked on the protractor and that is the width of the angle.