Complete Study of Supplementary Angles and Complementary Angles

Supplementary angle is a concept studied in geometry. In real life, supplementary angles are in stars, cups, and logos. In the Latin language, the word supplementary refers to suppliers here meaning supply, and place means fill. In simple language, it means when supplied to complete a thing.

  Supplementary angles are defined as a pair of any two angles that form a straight angle that is equal to 180 degrees. The pair of angles should be put together to form supplementary angles. The two angles measure up to 180 degrees. An example of supplementary angles is angle 1 and angle 2 is supplementary angles if angle 1 + angle 2 are a supplement to each other that is their sum is 180 degrees when put together.

Supplementary angles can be either adjacent or non-adjacent angles.

  1. Adjacent supplementary angles= Two angles are said to be adjacent supplementary angles if they have a common vertex and a common arm.
  2. Non-adjacent supplementary angles- Non-adjacent supplementary angles are the ones that neither have a common arm or a common vertex.

The supplementary angle can never be a pair of acute angles as acute angles measure less than 90°. If acute angles combined their sum would never be 180 degrees.

Example= X + y can never be supplementary angles as X and y are two acute angles.

X is equal to 40 degrees and y is equal to 60° if we add X and y that is 60 degrees + 40 degrees then the sum is 100° that is not equal to 180 degrees hence two acute angles can never be supplementary angles.

Two obtuse angles can never be supplementary as the measure of obtuse angles is more than 90 degrees and less than 180 degrees.

Two right angles occurring as pairs put together can form a supplementary angle. The value of a right angle is 90° so if we add two right angles that are 90 degrees + 90 degrees, the sum is equal to 180 degrees.

The complementary angles measures 90°. The complement of an angle x (90 – x).

Supplement of an angle X is (180 – X)

The concept of supplementary angles and their formula is used to solve many problems related to different shapes in geometry and algebra. The study of supplementary angles and complementary angles is used to determine the value of the angles when together.

 If you want to find a supplement of angle then the following formula is used-

   Where X degrees + y degrees= 180 degrees

    Y equal to (180 – X degrees)

    X is equal to 90°

    Y =?

    To find the value of Y we put the formula

    Y is equal to (180 – X degrees)

    Therefore y = 180 – 90 degrees

    Y = 90 degrees

    In real life, the complementary angle concept is used indoors, things with four edges like television. This concept is also used in the field of architecture where two lines are perpendicular to each other. The concept of complementary angle is also used to study squares and rectangles. In the square, each angle measures up to 90 degrees. In a rectangle, each angle measures 90 degrees again.


   X+ y = 90 degrees

   The formula to find complementary angle is

   Y = 90 degrees- X degrees

Example:    If x is equal to 60°

   Y =?

   Then y = (90 degrees- X degrees)

   Y = 90 degrees- 60 degrees

   Y = 30 degrees

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 Complementary angle is taken from the Latin word “complere” meaning complete. Complementary angles are a set of two angles at measure up to 90 degrees. A piece of bread is a rectangle in shape when cut into half along the diagonal results in triangles. Two acute angles are put together to form complementary angles. Complementary angles can be adjacent angles or non-adjacent angles. Adjacent complementary angles have a common arm and common vertex.

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