# Supplementary angles

The **supplementary angles** are the kind of angle at which their angles between achieve adding **180 ****degrees** different making the complementary angles that are only 90 degrees. Following the **property** and **formula** of the angles that complement each other, when an **angle** has less than 180 degrees, then it will correspond to an angle that supplements it according to the formula A ( **supplementary angle** ) = 180 ° minus (-) the angle that needs to be **supplemented** . Example: A = 180 ° – 150 ° = 30 °. The supplement of an angle of 45 ° is another of 135 °. The supplementary of an angle of 179 ° would then be an angle of 1 ° and the **supplementary** An angle measuring 90 ° is another of the same measure.

## What is a supplementary angle?

We define supplementary angles as those angles whose joint measures manage to reach **180** °. It is important to mention that two angles do not have to be **adjacent** to be **supplementary** .

- Definition
- How are supplementary angles obtained?
- features
- Trigonometric ratios of supplementary angles
- Examples

## Definition

Supplementary angles are the angles that when added together, achieve a figure of **180** ° so that **angle A** and **angle B** add up to a total of 180 °.

The application that supplementary angles have in practice or in daily life is very **technical** , it is special for calculating **architectural angles** and is very important in **construction** , because when segmenting a circumference it is possible to create a diameter line and divide it at any point obtaining, in order to achieve an angle with its **supplement** .

We can see supplementary angles reflected in our **daily lives** , for example, on the **hands** of a **watch** that constantly creates different **complementary angles** . Supplementary angles are also common in those structures that must support heavy weights, such as **a circus tent** , which must be fixed to the floor or a flat surface, and the rope must be tied to the stake at an angle. , which supplements the remaining space to the ground. On **arch bridges**You can also see supplementary angles in the bases, just as they form an angle that is supplemented with the other formed in a vacuum. A beam perpendicular to the ground can form two complementary angles to each other.

## How are supplementary angles obtained?

To obtain the supplementary angle **β** of a given angle **α** , a subtraction must be performed, so that:

**Β = 180 ° – α**

## features

The main characteristics of supplementary angles are the following:

- If two angles add up to 180 °, then we say that they
**supplement**. - They are angles that when added together, result in two
**right angles**. - It must be remembered that complementary angles are
**equivalent**to a right angle. - We can find them in
**structures**of all kinds, but mainly in those that must support a lot of**weight**. - When two angles are supplementary to two other angles that are
**congruent**or have the same measure, then the**supplementary**angles are also congruent with each other. - The
**sinuses**of the supplementary angles are the same. - The
**cosines**of the supplementary angles are of equal absolute value , but of inverse sign.

## Trigonometric ratios of supplementary angles

The trigonometric ratios of the angles are as follows:

**Sine**of the supplementary angle: sin (180 ° – α) = sin α**Cosine**of the supplementary angle: cos (180 ° – α) = -cos α**Tangent**of the supplementary angle: tan (180 ° – α) = tan α**Cosecant**of the supplementary angle: csc (180 ° – α) = csc α**Secant**of the supplementary angle: sec (180 ° – α = -sec α**Cotangent**of the supplementary angle: cot (180 ° – α) = -cot α

## Examples

Let’s remember in order to give examples that the supplementary angles must add up to a total of **180** °. For example, if we have two angles that measure 140 ° and 40 ° respectively, we know that these are supplementary angles, since the total sum of their angles is equal to 180 °, then we can say that the following are examples of supplementary angles :

- What is the supplementary angle to a
**60 degree**angle ? An angle of**120 degrees**. - What is the supplementary angle to a
**20 degree**angle ? An angle of**160 degrees**.