We explain what an angle is, its types, and its characteristics. Also, add, subtract, multiply, and divide with tips and how to measure them.

**What is the angle?**

The angle is the portion of the plane between two rays (sides) with a common origin called the vertex. The tips start from a point and have two lines coming out from that point and creating an opening represented by an arc. The angle represents the degree of space of these arches (and not their extension).

The concept of angle corresponds to geometry, one of the branches of mathematics, but it is also applied in other fields such as engineering, optics, or astronomy.

Angles are measured using 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 circumference. For example: In a clock face, the hands form angles. At noon, when the two arrows point to the same side, the tip is 0°; at 3 o’clock, 90°; at 6 o’clock, 180° and at 9 o’clock, 270°.

The angles are represented by a magnitude that can be analyzed and compared with others, so there are operations between grades. Tips can be added and subtracted from each other or multiplied and divided by whole numbers.

The line that divides an angle into two equal parts is called a bisector, and any point on it is equidistant from both sides of the curve.

**types of angles**

Angle – Mathematics

A zero angle measures 0°.

Angles can be classified according to specific criteria.

**According to its width:**

- 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 relation with another angle:**

Supplementary angles. They are angles that add up to 180 degrees.

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 successive angles, and the side 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.

**Operations with angles**

Sums between angles. When adding two or more angles, add the degrees (and also the minutes and seconds, if applicable) of each angle. For example:

angle α + angle β = angle γ

90º + 70º = 160º

Subtraction between angles. When two or more angles are subtracted, each angle’s degrees (and also the minutes and seconds, if applicable) must be subtracted. For example:

angle γ – angle β = angle α

160º – 70º = 90º

Multiplications with angles. When multiplying a tip by a natural number, multiply the degrees, minutes, and seconds by that number. If the values of the minutes or seconds exceed 60, those 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 a tip by a natural number, divide the degrees, minutes, and seconds by that number. In the beginning, the degrees are divided by the number, and the rest obtained is transformed into minutes (by multiplying it by 60) and added to the minutes we already had. The minutes are divided, and the rest is added to the seconds we already had, separated.

**How is an angle measured?**

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 made of plastic. The steps to measure an angle are as follows:

1. The center of the protractor, indicated by a slot, should be placed at the angle’s vertex (the origin of the angle).

2. It must be verified that one of the angle’s sides coincides with the base of the protractor.

3. The graduation of the remaining side is marked on the protractor, which is the angle’s width.