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


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 bridgesYou 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


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


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 .

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